objective Ques (152 results)
SSC CGL Mains 20241)
11 : 15
SSC CGL Mains 20242)In a triangle HJK, HJ = HK. G is a point on HJ such that HG = GK = JK. What is the degree measure of two-third of (∠HGK + ∠GKJ)?
96°
SSC CGL Mains 20243)∆ABC is inscribed in a circle with Centre O. If AB = 21 cm, BC = 20 cm and AC = 29 cm, then what is the length of the circumradius of the triangle?
14.5 cm
SSC CGL 20224)If the areas of two isosceles triangles are in the ratio of x2 ∶ y2, then the ratio of their corresponding heights is:
x ∶ y
, Avg: 00:53 , 100%✓ SSC CGL 20225)What is the ASA congruence rule of triangles, where A and S represents angle and side of triangle respectively?
Two triangles are said to be congruent if 2 angles and the included side of one triangle are equal to 2 angles and the included side of the other triangle.
SSC CGL 20226)
△ABC is a right-angle triangle at B and tan A = \(\frac{3}{4} \), then sin A + sin B + sin C will be equal to:
\(2\frac{2}{5}\)
SSC CGL 20227)If ∆ABC ~ ∆EDF such that AB = 6 cm, DF = 16 cm and DE = 8 cm, then the length of BC is:
12 cm
, Avg: 01:30 , 88%✓ SSC CGL 20228)In ∆ ABC, D and E are points on sides AB and AC, such that DE ΙΙ BC. If AD = x + 3, DB = 2x − 3, AE = x + 1 and EC = 2x − 2, then the value of x is:
\({{3} \over 5}\)
SSC CGL 20229)In ΔPQR, ∠Q = 90°, PQ = 8 cm and ∠PRQ = 45°. Find the length of QR.
8 cm
SSC CGL 202210)ΔABC ~ ΔDEF and the perimeters of these triangles are 32 cm and 12 cm, respectively. If DE = 6 cm, then what will be the length of AB?
16 cm
, Avg: 01:21 , 100%✓ SSC CGL 202211)ΔABC and ΔDEF are similar triangles and their areas are 49 cm2 and 144 cm2 respectively. If EF = 16.80 cm, then find BC.
9.8 cm
, Avg: 00:51 , 50%✓ SSC CGL 202212)If ΔABC ≅ ΔPQR and ∠ABC = (x + 60)°, ∠PQR = (85 - 4x)°, and ∠RPQ = (3x + 65)°, then the value of ∠ABC in degree is:
65
, Avg: 00:32 , 100%✓ SSC CGL 202213)An airplane goes 14 km due east and then 48 km due north. How far is it from its initial position?
50 km
, Avg: 00:36 , 100%✓ SSC CGL 202214)The side of an equilateral triangle is 9 cm. What is the radius of the circle circumscribing this equilateral triangle?
\(3 \sqrt{3}\) cm
SSC CGL 202215)'O' is a point in the interior of an equilateral triangle. The perpendicular distance from 'O' to the sides are\( \sqrt3 cm\), 2 cm, 5 cm. The perimeter of the triangle is :
48 cm
, Avg: 01:01 , 75%✓ SSC CGL 202216)ΔPQR is right-angled at Q. The length of PQ is 5 cm and ∠PRQ = 30°. Determine the length of side QR.
\(5\sqrt3 cm\)
, Avg: 01:25 , 100%✓ SSC CGL 202217)Find the area of the shaded portion of an equilateral triangle with sides 6 units shown in the following figure. A circle of radius 1 unit is centred at midpoint of a side of the triangle.
\(\frac{1}{2}\left( {9\sqrt 3 - \frac{{11}}{7}} \right)\) \(unit^{2}\)
, Avg: 00:03 , 100%✓ SSC CGL 202218)In a Δ ABC, ∠B + ∠C = 110°, then find the measure of ∠A.
70°
, Avg: 01:13 , 100%✓ SSC CGL 202219)The area of a triangle is 480 cm2 and the ratio of its sides is 10 ∶ 24 26. What is the perimeter of the triangle?
120 cm
, Avg: 01:26 , 66%✓ SSC CGL 202220)In the given triangle, CD is the bisector of ∠BCA. CD = DA. If ∠BDC = 76°, What is the degree measure of ∠CBD?
66°
, Avg: 00:49 , 75%✓ SSC CGL 202221)In triangle ABC, the bisector of angle BAC cuts the line BC at D. If BD = 6 and BC = 14 then what is the value of AB : AC?
3 : 4
, Avg: 00:16 , 100%✓ SSC CGL 202222)From the following figure find x+ y + z.
120°
, Avg: 00:46 , 100%✓ SSC CGL 202223)If the figure, AB = AD = 7 cm and AC = AE and BC = 11 cm, then find the length of ED.
11
, Avg: 00:50 , 75%✓ SSC CGL 202224)If the angles of a triangle are (x - 46) degrees, (x + 96) degrees and 8x degrees, then what is the value of 2x?
26 degrees
, Avg: 01:08 , 50%✓ SSC CGL 202225)The side of an equilateral triangle is 12 cm. What is the radius of the circle circumscribing this equilateral triangle?
4√3 cm
, Avg: 00:51 , 100%✓ SSC CGL 202226)If areas of similar triangles ΔABC and ΔDEF are x2 cm2 and y2 cm2 respectively, and EF = a cm, then BC (in cm) is:
\(\frac{a x}{y}\)
SSC CGL 202227)In the triangle ABC, AB = 12 cm and AC = 10 cm, and ∠BAC = 60°. What is the value of the length of the side BC?
11.13 cm
, Avg: 00:47 , 100%✓ SSC CGL 202228)In a right-angled triangle PQR, right-angled at Q, the length of the side PR is 17 units, length of the base QR is 8 units, and length of the side PQ is 15 units. If ∠RPQ = α, then sin α + cos α is:
\(\frac{23}{17}\)
SSC CGL 202229)In ∆ABC, the perpendiculars drawn from A, B and C meet the opposite sides at points D, E and F, respectively. AD, BE and CF intersect at point P. If ∠EPD = 110° and the bisectors of ∠A and ∠B meet at point Q, then ∠AQB = ?
125°
, Avg: 01:15 , 33%✓ SSC CGL 202230)In the following figure, AD bisects angle BAC. Find the length (in cm) of BD.
4
, Avg: 01:13 , 50%✓ SSC CGL 202231)In a triangle ABC, points P and Q are AB and AC, respectively, such that AP = 4 cm, PB = 6 cm, AQ = 5 cm and QC = 7.5 cm. If PQ = 6 cm, then find BC (in cm).
15
, Avg: 00:33 , 71%✓ SSC CGL 202232)In triangle ABC, the bisector of angle BAC meets BC at point D in such a way that AB = 10 cm, AC = 15 cm and BD = 6 cm. Find the length of BC (in cm).
15
, Avg: 01:12 , 100%✓ SSC CGL 202233)In a ΔABC, D, E and F are the mid-points of side BC, CA and AB respectively. If BC = 25.6 cm, CA = 18.8 cm and AB = 20.4 cm, what is the perimeter (in cm) of the ΔDEF?
32.4
, Avg: 01:42 , 50%✓ SSC CGL 202234)In a right-angled triangle PQR, ∠Q = 90°. A and B are the mid-points of PQ and PR, respectively. If PQ = 16 cm, QR = 30 cm and PR = 34 cm, what is perimeter (in cm) of the trapezium ABRQ?
70
, Avg: 00:21 , 57%✓ SSC CGL 202235)In △ABC, ∠A = 68°. If I is the incentre of the triangle, then the measure of ∠BIC is:
124°
SSC CGL 202236)In triangle ABC, X and Y are the points on sides AB and AC, respectively, such that XY is parallel to BC. If XY : BC = 2.5 : 7, what is the ratio of the area of the trapezium BCYX to that of the ΔAXY?
\(171\over25\)
, Avg: 02:53 , 100%✓ SSC CGL 202237)In ΔPQR, ∠Q = 66° and ∠R = 34. T is a point on QR , and S is a point between Q and T such that PS ⊥ QR and PT is the bisector of ∠QPR. What is the measure of ∠SPT?
16
, Avg: 00:39 , 100%✓ SSC CGL 202238)A triangle with the lengths of its sides proportional to the numbers 7, 24 and 30 is:
obtuse angled
SSC CGL 202239)In a right triangle ABC, right angled at B, altitude BD is drawn to the hypotenuse AC of the triangle. If AD = 6 cm, CD = 5 cm, then find the value of AB2 + BD2 (in cm).
96
, Avg: 00:39 , 33%✓ SSC CGL 202240)In a right-angled triangle, the lengths of the medians from the vertices of acute angles are 7 cm and \( 4\sqrt 6\) cm. What is the length of the hypotenuse of the triangle (in cm)?
\(2\sqrt{29}\)
, Avg: 01:02 , 62%✓ SSC CGL 202241)In a triangle ABC, the bisector of angle BAC meets BC at point D such that DC = 2BD. If AC - AB = 5 cm, then find the length of AB (in cm).
5
, Avg: 02:14 , 50%✓ SSC CGL 202242)A circle is inscribed in ΔABC, touching AB, BC and AC at the points P, Q and R, respectively: If AB - BC = 4 cm, AB - AC = 2 cm and the perimeter of ΔABC = 32 cm, then \(BC \over 2\) (in cm) = ?
\(13 \over 3\)
, Avg: 01:57 , 60%✓ SSC CGL 202243)In ΔABC, ∠A = 66°, BD ⊥ AC and CE ⊥ AB. BD and EC intersect at P. The bisectors ∠PBC and ∠PCB meet at Q. What is the measure of ∠BQC?
147°
, Avg: 00:44 , 66%✓ SSC CGL 202244)The circumcentre of an equilateral triangle is at a distance of 3.2 cm from the base of the triangle. What is the length (in cm) of each of its altitudes?
9.6
, Avg: 01:24 , 66%✓ SSC CGL 202245)Let ΔABC ~ ΔQPR and (Area of ΔABC) : (Area of ΔPQR) = 121 : 64. If QP = 14.4 cm, PR = 12 cm and AC = 18 cm, then what is the length of AB?
19.8 cm
, Avg: 01:23 , 85%✓ SSC CGL 202246)In a ΔABC, D, E and F are the mid-points of side BC, CA and AB respectively. If BC = 14.4 cm, CA = 15.2 cm and AB = 12.4 cm, what is the perimeter (in cm) of the ΔDEF?
21
SSC CGL 202247)In Δ PQR, S is a point on the side QR such that PS is the bisector of ∠QPR. If PQ = 12 cm, QS = 3 cm and QR = 7 cm, then what is the length of side PR?
18 cm
, Avg: 00:15 , 85%✓ SSC CGL 202248)The area of similar triangles PQR and MNT are 196 cm2 and 169 cm2 respectively. If the longest side of the larger Δ PQR be 28 cm then what is the length (in cm) of the longest side of the smaller Δ MNT?
26
, Avg: 01:09 , 71%✓ SSC CGL 202249)In ΔABC, AB = 7 cm, BC = 10 cm, and AC = 8 cm. If AD is the angle bisector of ∠BAC, where D is a point on BC, then \( \frac{DC}{4}\) (in cm) is equal to:
\(4\over 3\)
, Avg: 00:54 , 70%✓ SSC CGL 202250)The sides AB and AC of ΔABC are produced to points D and E, respectively. The bisectors of ∠CBD and ∠BCE meet at P. If ∠A = 88°, the measure of ∠P is :
46°
, Avg: 00:49 , 50%✓ SSC CGL 202251)In a ΔABC, the bisector of ∠A meets BC at D. If AB = 9.6 cm, AC = 11.2 cm and BD = 4.8 cm, the perimeter (in cm) of ΔABC is:
31.2
, Avg: 02:03 , 80%✓ SSC CGL 202252)A circle is inscribed in ΔABC, touching AB, BC and AC at the points P, Q and R, respectively. If AB - BC = 4 cm, AB - AC = 2 cm, and the perimeter of ΔABC = 32 cm, then AC (in cm) = ?
\(\frac{32}{3}\)
, Avg: 00:52 , 87%✓ SSC CGL 202253)Let ΔABC ~ ΔPQR and \(\frac{\operatorname{ar}(\triangle \mathrm{ABC})}{\operatorname{ar}(\triangle \mathrm{QPR})}=\frac{64}{169} \text { }\). If AB = 10 cm, BC = 7 cm and AC = 16 cm, then PR (in cm) is equal to:
26
, Avg: 01:26 , 87%✓ SSC CGL 202254)The sides PQ and PR of ΔPQR are produced to points S and T, respectively. The bisectors of ∠SQR and ∠TRQ meet at point U. If ∠QUR = 69°, then the measure of ∠P is:
42°
, Avg: 00:44 , 77%✓ SSC CGL 202255)The base of a triangle is increased by 40%. By what percentage (correct to two decimal places) should its height be increased so that the area increases by 60%?
14.29%
, Avg: 01:35 , 33%✓ SSC CGL 202256)In ΔABC, D is a point on side BC such that ∠ADC = ∠BAC. If CA = 15 cm and CD = 9 cm, then CB (in cm) = ?
25
, Avg: 00:45 , 100%✓ SSC CGL 202257)In ΔABC, AB = 7 cm, BC = 10 cm, and AC = 8 cm. If AD is the angle bisector of ∠BAC, where D is a point on BC, then DC (in cm) = ?
\(\frac{16}{3}\)
, Avg: 02:55 , 80%✓ SSC CGL 202258)In a triangle ABC, D and E are points on BC such that AD = AE and ∠BAD = ∠CAE. If AB = (2p + 3), BD = 2p, AC = (3q - 1) and CE = q, then find the value of (p + q).
3
, Avg: 01:19 , 28%✓ SSC CGL 202259)In Δ ABC, D is a point on side BC such that ∠ADC = ∠BAC. If CA = 12 cm, CD = 8 cm, then CB (in cm) = ?
18
, Avg: 00:26 , 100%✓ SSC CGL 202260)In Δ ABC, AD is perpendicular to BC and AE is the bisector of ∠ BAC. If ∠ABC = 58° and ∠ACB = 34°, then find the measure of ∠DAE.
12°
, Avg: 00:39 , 85%✓ SSC CGL 202261)The angles of a triangle are (8x - 15)°,(6x - 11)° and ( 4x – 10)°. What is the value of x ?
12
, Avg: 01:13 , 85%✓ SSC CGL 202262)Sides AB and AC of ∆ ABC are produced to points D and E, respectively. The bisectors of ∠CBD and ∠BCE meet at P. If ∠A = 78°, then the measure of ∠P is:
51°
, Avg: 00:38 , 83%✓ SSC CGL 202263)In ∆ ABC, ∠A = 88°. If I is the incentre of the triangle, then the measure of ∠BIC is:
134°
, Avg: 00:46 , 77%✓ SSC CGL 202264)The bisector of ∠B in ΔABC meets AC at D. If AB = 12 cm, BC = 18 cm and AC = 15 cm, then the length of AD (in cm) is:
6
, Avg: 00:52 , 50%✓ SSC CGL 202265)The difference between the two perpendicular sides of a right-angled triangle is 17 cm and its area is 84 cm2. What is the perimeter (in cm) of the triangle?
56
, Avg: 00:49 , 100%✓ SSC CGL 202266)In Δ LMN, the bisector of ∠L and ∠N intersect at and angle of 112°. What is the measure (in degree) of ∠M?
44
, Avg: 01:30 , 71%✓ SSC CGL 202267)In ΔACD, B and E are two points on side AC and AD respectively, such that BE is parallel to CD. CD = 9 cm, BE = 6 cm, AB = 5 cm and ED = 2 cm. What are the measures of the lengths (in cm) of AE and BC?
4, 2.5
, Avg: 00:26 , 100%✓ SSC CGL 202268)What is the height (in cm) of an equilateral triangle whose each side is 8 cm?
4√3
, Avg: 00:54 , 50%✓ SSC CGL 202269)The lengths of the three sides of a right-angled triangle are (x - 1) cm, (x + 1) cm and (x + 3) cm, respectively. The hypotenuse of the right-angled triangle (in cm) is:
10
, Avg: 00:58 , 33%✓ SSC CGL 202270)An equilateral triangle ABC is inscribed in a circle with centre O. D is a point on the minor arc BC and ∠CBD = 40º. Find the measure of ∠BCD.
20º
, Avg: 02:24 , 43%✓ SSC CGL 202271)In a ΔABC, points P, Q and R are taken on AB, BC and CA, respectively, such that BQ = PQ and QC = QR. If ∠BAC = 75º, what is the measure of ∠PQR (in degrees)?
30
SSC CPO 202072)The sides PQ and PR of ΔPQR are produced to points S and T, respectively. The bisectors of ∠SQR and ∠TRQ meet at U. If ∠QUR = 59°, then the measure of ∠P is:
62°
SSC CPO 202073)In ΔABC, ∠A = 54°. If I is the incentre of the triangle, then the measure of ∠BIC is:
117°
SSC CPO 202074)A circle is inscribed in a triangle ABC. It touches side AB, BC, and AC at points R, P, and Q respectively. If AQ = 2.6 cm, PC = 2.7 cm and BR = 3 cm, then the perimeter (in cm) of the triangle ABC is:
16.6
SSC CPO 202075)In ΔABC, BD ⊥ AC at D, E is a point on BC such that ∠BEA = x°. If ∠EAC = 62° and ∠ EBD = 60°, then the value of x is:
92°
, Avg: 01:08 , 66%✓ SSC CPO 202076)In ΔABC, ∠A = 68°. If I is the incentre of the triangle, then the measure of ∠BIC is:
124°
, Avg: 00:41 , 25%✓ SSC CPO 202077)In ΔABC, D is the median from A to BC. AB = 6 cm, AC = 8 cm, and BC = 10 cm. The length of median AD (in cm) is:
5
, Avg: 01:21 , 100%✓ SSC CPO 202078)The perimeter of a right triangle is 60 cm and its hypotenuse is 26 cm. What is the area (in cm2) of the triangle?
120
, Avg: 01:36 , 100%✓ SSC CPO 202079)Let Δ ABC ∼ Δ RPQ and \(\frac{{ar(\Delta ABC)}}{{ar(\Delta RPQ)}} = \frac{4}{9}\) . If AB = 3 cm, BC = 4 cm and AC = 5 cm, then RP (in cm) is equal to:
4.5 cm
, Avg: 00:39 , 100%✓ SSC CPO 202080)In ΔABC, AB and AC are produced to points D and E, respectively. If the bisectors of ∠CBD and ∠BCE meet at the point O, and ∠BOC = 57°, then ∠A is equal to:
66°
, Avg: 01:14 , 100%✓ SSC CPO 202081)In ΔABC,∠A = 66°. AB and AC are produced to points D and E, respectively. If the bisectors of angle CBD and angle BCE meet at the point O, then∠BOC is equal to:
57°
, Avg: 00:11 , 100%✓ SSC CPO 202082)LetΔABC ~ΔRPQ and \(\frac {ar (\Delta ABC)}{ar(\Delta RPQ)} = \frac 4 9 \). If AB = 3 cm, BC = 4 cm and AC = 5 cm, then PQ (in cm) is equal to:
6
, Avg: 01:00 , 60%✓ SSC CPO 202083)In ΔABC, BD ⊥ AC at D, E is a point on BC such that ∠BEA = x°. If ∠EAC = 46° and ∠EBD = 60°, then the value of x is:
76°
, Avg: 00:58 , 59%✓ SSC CHSL 202184)In Δ ABC, AC = BC, and the length of the base AB is 10 cm. If CG = 8 cm, where G is the centroid, then what is the length of AC?
13 cm
, Avg: 00:41 , 100%✓ SSC CHSL 202185)The sum of all the three sides of an equilateral triangle is 15√3 cm. The height of the triangle is:
7.5 cm
, Avg: 01:05 , 83%✓ SSC CHSL 202186)The area of an equilateral triangle is 10.24√3 m2. Its perimeter (in m) is:
19.2
, Avg: 01:23 , 100%✓ SSC CHSL 202187)The side QR of a triangle PQR is extended to a point S. If ∠PRS = 104° and ∠RQP =\(\frac{3}{5}\)∠QPR, then the value of ∠QPR is:
65°
, Avg: 01:51 , 100%✓ SSC CHSL 202188)In Δ ABC, AD is the bisector of ∠A meeting BC at D. If AB = 15 cm, BC = 10 cm and the length of BD is 2 cm less than that of DC , then the length of AC is:
22.5 cm
, Avg: 01:11 , 60%✓ SSC CHSL 202189)In ΔABC, P and Q are the mid-points of the sides AB and AC, respectively. R is a point on the segment PQ such that PR ∶ RQ = 1 ∶ 3. If PR = 4 cm, then BC is equal to:
32 cm
, Avg: 00:56 , 66%✓ SSC CHSL 202190)The sum of three sides of an isosceles triangle is 20 cm, and the ratio of an equal side to the base is 3 ∶ 4. The altitude of the triangle is:
2√5 cm
, Avg: 03:13 , 60%✓ SSC CHSL 202191)In a triangle ABC, the length of side AC is 4 cm less than five times the length of side AB. The length of side BC exceeds four times the length of side AB by 4 cm. If the perimeter of Δ ABC is 90 cm, then its area is:
180 cm2
SSC CHSL 202192)If Δ ABC∼Δ QPR,\( \rm \frac{ar(\Delta ABC)}{ar(\Delta PQR)}=\frac{4}{9}\), AC = 12 cm, AB = 18 cm and BC = 10 cm, then PR (in cm) is equal to:
15
, Avg: 00:44 , 100%✓ SSC CHSL 202193)If O is the centroid and RP is the median with length 24 cm of Δ RST , where P is a point on ST, then the value of RO is:
16 cm
, Avg: 01:26 , 50%✓ SSC CHSL 202194)The sides AB, BC and AC of ΔABC are 12 cm, 8 cm and 10 cm, respectively. A circle is inscribed in the triangle touching AB, BC and AC at D, E and F, respectively. The ratio of the lengths of AD to CE is:
7 ∶ 3
, Avg: 01:04 , 66%✓ SSC CHSL 202195)In ΔPQR, QT ⊥ PR and S is a point on QR such that ∠PSQ = p°. If ∠TQR = 44° and ∠SPR = 32°, then the value of p is:
78°
, Avg: 01:08 , 33%✓ SSC CHSL 202196)The sides of a triangle are in the ratio \(\frac{1}{3},\frac{1}{5},\frac{1}{4}\) and its perimeter is 141 cm. The difference between the greatest side and the smallest side is:
24 cm
, Avg: 00:41 , 100%✓ SSC CHSL 202197)In any triangle, if the angles are in the ratio 1 : 2 : 3, then what will be the ratio of the sides opposite to them?
1 : √3 : 2
, Avg: 03:09 , 33%✓ SSC CHSL 202198)If S is a point on side QR of a triangle PQR such that QS = 10 cm, QR = 18 cm and ∠PSR = ∠QPR, then the length of PR will be:
12 cm
, Avg: 00:47 , 66%✓ SSC CHSL 202199)In Δ ABC, points D and E are on AB and AC, respectively, such that DE is parallel to BC. IE AD = 3 cm, BD = 6 cm and AE = 2 cm, then find the length of CE.
4 cm
, Avg: 01:03 , 100%✓ SSC CHSL 2021100)ABC is a triangle inscribed in a circle and ∠ACB is equal to 35°. P is a point on the circle on the side AB, opposite to C. What is the value of ∠APB in degrees?
145
, Avg: 01:31 , 50%✓ SSC CHSL 2021101)In triangle ABC, AD is the internal bisector of \(\angle A\) meeting BC at D. If BD = 3.6 cm and BC = 8 cm, then the ratio of AB to AC will be:
9 ∶ 11
, Avg: 01:44 , 28%✓ SSC CHSL 2021102)In a circle, two chords UV and WX intersect each other at a point Z within the circle. If UV = 18 cm, ZV = 6 cm and WZ = 9 cm, then the length of ZX is:
8 cm
, Avg: 01:49 , 66%✓ SSC CHSL 2021103)Chords AB and CD of a circle intersect externally at P. If AB = 8.8 cm, PB = 7.2 cm, PD = 6.4 cm, then CD is equal to:
11.6 cm
, Avg: 02:01 , 50%✓ SSC CHSL 2021104)AB is the diameter of a circle of radius 9 cm. PQ is a chord (not a diameter) that intersects AB at M perpendicularly. If AM : BM = 5 : 4, then the length of chord PQ will be:
8√5 cm
SSC CHSL 2021105)AB is 12 cm long chord of a circle with centre O and radius 10 cm. The tangents at A and B intersect at P. What is the length of OP?
12.5 cm
, Avg: 00:40 , 50%✓ SSC CHSL 2021106)A circle touches the side BC of ΔABC at P and also touches AB and AC produced at Q and R, respectively. If the perimeter of ΔABC = 14.1 cm, then the length (in cm) of AQ will be:
7.05
, Avg: 00:24 , 75%✓ SSC CHSL 2021107)Two circle touch each other externally. The distance between their centres is 14 cm. If the radius of one circle is 8 cm, then the radius of the other circle is:
6 cm
, Avg: 01:12 , 50%✓ SSC CHSL 2021108)The circumference of a circle is 'aπ' units and the area of the circle is 'bπ' square units. If a ∶ b is equal to 4 ∶ 5, then the radius of the circle is:
2.5 cm
SSC CHSL 2021109)Chord AB of a circle with radius 5 cm is at a distance of 4 cm from the centre O. If tangents drawn at A and B intersect at P, then find the length of the tangent AP.
3.75 cm
SSC CHSL 2021110)In a circle with center O, APB is a tangent at P. If MN is a diameter such that ∠ BPN = 52°, then what is the measure of ∠ PNM?
38°
, Avg: 00:47 , 50%✓ SSC CHSL 2021111)Points A, B, C and D are concyclic points of a circle with centre O, such that ∠DOC = 73°. The measure of ∠AOC is 215°. What is the measure of ∠ AOD?
72°
, Avg: 00:53 , 100%✓ SSC CHSL 2021112)PA and PB are tangents drawn to a circle with centre O from an external point P. If A and B are points on the circle and ∠OBA = 42°, then ∠APB is:
84°
, Avg: 01:32 , 62%✓ SSC CHSL 2021113)Two chords PQ and RS of a circle meet at A when produced. AT is a tangent to the circle meeting it at T. The ratio PA : SA is equal to which of the following?
RA : AQ
, Avg: 00:52 , 100%✓ SSC CHSL 2021114)The distance between two equal parallel chords of a circle is 10 cm. If the chords are 24 cm long, then what is the length of the radius?
13 cm
, Avg: 00:20 , 100%✓ SSC CHSL 2021115)Two circles of radii 4 cm and 3 cm, respectively, touch each other externally. What is the distance (in cm) between their centres?
7
, Avg: 00:34 , 100%✓ SSC CHSL 2021116)A circle is inscribed in a triangle ABC. It touches sides AB, BC and AC at points R, P and Q, respectively. If AQ = 6.5 cm, PC = 7.5 cm and BR = 9 cm, then the perimeter (in cm) of the triangle ABC will be:
46
, Avg: 00:36 , 100%✓ SSC CHSL 2021117)If PA and PB are tangents drawn to a circle with centre O at A and B from external point P such that ∠APB = 78°, then ∠OAB is equal to:
39°
SSC CHSL 2021118)In a circle, AB and DC are two chords. When AB and DC are produced, they meet at P. If PC = 2.8 cm, PB = 3.15 cm and AB = 3.85 cm, then CD = ?
5.075 cm
, Avg: 03:12 , 66%✓ SSC CHSL 2021119)A chord PQ of a circle C1 of radius 9.25 cm touches another circle C2 that is concentric to C1, and the radius of C2 is 3 cm. What is the length (in cm) of PQ?
17.5
, Avg: 01:38 , 25%✓ SSC CHSL 2021120)Chords AB and CD of a circle are produced to meet at the point P, outside the circle, and AD is the diameter of the circle. If ∠DAP = 36° and ∠APC = 30°, then what will be the measure of ∠CBD?
24°
, Avg: 00:41 , 33%✓ SSC CHSL 2021121)Two concentric circles are of radii 15 cm and 6 cm. What is the length (in cm) of the chord of the larger circle that is tangent to the smaller circle?
6√21
SSC CHSL 2021122)AB is a chord of a circle with centre O and P is any point on the circle. If ∠APB = 112°, then what is the measure of ∠OAB ?
22°
, Avg: 00:48 , 70%✓ SSC CHSL 2021123)A and B are two points on a circle with centre O. C is a point on the minor arc of the circle between points A and B. The tangents to the circle at A and B meet each other at a point D. If ∠ ADB = 25°, then ∠ ACB (in degrees) is equal to :
102.5
, Avg: 01:00 , 50%✓ SSC CHSL 2021124)AB is a diameter of the circle with centre 0. The tangent at the point C on the circle meets AB produced at Q. If ∠BAC = 34°, then the measures of ∠CQA (in degrees) will be:
22
, Avg: 00:44 , 66%✓ SSC CHSL 2021125)AB is a diameter of a circle with centre O. If C is any point on the circle such that ∠BAC = 42°, then find the measure of ∠BOC.
84°
, Avg: 01:30 , 42%✓ SSC CHSL 2021126)P, Q and R are three points on the circumference of a circle such that QR is a diameter and PQ = PR. If the radius of the circle is 7 cm. then the length of PQ is:
7√2 cm
, Avg: 01:48 , 25%✓ SSC CHSL 2021127)AB and CD are two chords of a circle that intersects at E inside the circle. If ∠BEC = 125° and ∠EBD = 28°, then what is the measure of ∠BAC?
97°
, Avg: 00:32 , 92%✓ SSC CHSL 2021128)Let O be the centre of a circle. PA and PB are tangents to the circle from a point P outside the circle and A and B are points on the circle. If angle APB = 50°, then angle OAB is equal to:
25°
, Avg: 01:05 , 100%✓ SSC CHSL 2021129)AB and AC are tangents to a circle with centre O from an external point A. The tangents AB and AC touch the circle at B and C, respectively, such that ∠BAC = 118°. Find the measures of ∠OCB.
59°
, Avg: 00:09 , 74%✓ SSC CHSL 2021130)In a circle with centre O, a 6 cm long chord is at a distance 4 cm from the centre. Find the length of the diameter.
10 cm
, Avg: 01:06 , 62%✓ SSC CHSL 2021131)Chord AB and diameter CD of a circle meet at the point P, outside the circle when the produced, If PB = 8 cm, AB = 12 cm and distance of P from the centre of the circle is 18 cm, the radius (in cm) of the circle is closest to:
12.8
, Avg: 00:04 , 40%✓ SSC CGL 2020132)Two chords AB and CD of a circle with centre O intersect each other at P. If \(\angle APC = 95^0\) and \(\angle AOD = 110^0\) , then \(\angle BOC\) is:
\(60^0\)
For an equal arc, angle at the centre = 2 \(\times\) angle at the circumference ;
\(\therefore \angle AOD =2\angle ABD\); ⇒ \(\angle ABD = {110^0\over2}= 55^0= \angle PBD\) ;
\(\angle APC = \angle BPD = 95^0\);
In \(\triangle PBD\), \(\angle BPD +\angle PDB+\angle PBD = 180^0\) ; ⇒ \(\angle BDP= 180-95-55= 30^0\) ;
\(\therefore \angle BOC = 2\times \angle BDP = 2\times 30= 60^0\)
, 40%✓ SSC CGL 2020133)Diameter AB of a circle with centre O is produced to a point P such that PO = 16.8 cm. PQR is a secant which intersects the circle at Q and R, such that PQ = 12 cm and PR = 19.2 cm.The length of AB (in cm.) is :
14.4
PQ = 12 cm ; PR = 19.2 cm ; PO = 16.8 cm ; Let, OA = OB = x ;
BP x AP = PQ x PR ; ⇒ (16.8 - x)(16.8 + x) = 12 x 19.2 ; x = 7.2 cm.
\(\therefore AB=2\times7.2 = 14.4cm\)
, Avg: 00:09 , 67%✓ SSC CGL 2020134)In the given figure, \(\angle KLN = 58^0\), then \(\angle KMN=\space?\)
\(58^0\)
\(\angle KLN = 58^0\) ; \(\therefore \angle KMN = 58^0\) ;
Because angles in the same segment are equal.
, Avg: 00:43 , 77%✓ SSC CGL 2020135)In the figure, two circles with centres P and Q touch externally at R. Tangents AT and BT meet the common tangent TR at T. If AP = 6 cm and PT = 10 cm, then BT = ?
8 cm
In \(\triangle PAT\) \(\angle PAT = 90^0\);
\(\therefore AT= \sqrt{ PT^2-AP^2} = \sqrt{10^2-6^2}= 8cm\);
Tangent drawn from an external point to a circle are equal.
\(\therefore\) AT = BT = 8 cm
, Avg: 01:08 , 85%✓ SSC CGL 2020136)Two tangents PA and PB are drawn to a circle with centre O from an external point P. If \(\angle OAB = 30^0\), then \(\angle APB\) is:
\(60^0\)
\angle OAB = \(30^0\); OA = OB = radii of circle; \(\angle OAB = \angle OBA = 30^0\); \(\angle AOB = 180^0-(30^0+30^0)=120^0\); In quadrilateral OAPB, \(\therefore\angle OAP = \angle OBP = 90^0\); \(\therefore \angle AOB +\angle APB = 180^0\); ⇒\(\angle APB = 180-120 =60^0\)
, Avg: 00:22 , 86%✓ SSC CGL 2020137)In the given figure, if \(\angle APO = 35^0\), then which of the following options is correct?
\(\angle BPO = 35^0\)
Join OA and OB. Since OA = OB ; AP = PB and OP is common. Therefore, triangle AOP is similar to triangle BOP. Since angle OAP = 90 & OBP = 90. Therefore, \({OAP\over OBP} ={APO\over BPO}\); ⇒ \({90\over90}={35\over BPO}\); ⇒ BPO = \(35^0\)
, Avg: 00:44 , 46%✓ SSC CGL 2020138)In the given figure, if AB = 10 cm, CD = 7 cm, SD = 4 cm and AS = 5 cm, then BC = ?
8 cm
SD = 4cm; So DR = 4 cm ; CR = CQ = 7 - 4 = 3 cm; AS = 5 cm ; AS = AP = 5 cm ; AB = 10 cm ; BP = BQ = 10 - 5= 5 cm; So BC = BQ + CQ = 5 + 3 = 8 cm
, Avg: 00:56 , 66%✓ SSC CGL 2020139)A, B and C are three points on a circle such that the angle subtended by the chords AB and AC at the centre O are \(80^0\) and \(120^0\), respectively. The value of \(\angle BAC\) is:
\(80^0\)
\(\angle AOB = 80^0\); \(\angle AOC = 120^0\); \(\therefore \angle BOC = 360^0-(80^0+120^0)=160^0\) \(\therefore \angle BAC = {\angle BOC\over2}={160^0\over2} = 80^0\)
, Avg: 01:26 , 85%✓ SSC CGL 2020140)In the given figure, MP is a tangent to a circle with center A and NQ is a tangent to a circle with center B. If MP = 15 cm, NQ = 8 cm, PA = 17 cm and BQ = 10 cm, then AB is:
14 cm.
PA = 17 ; PM = 15 cm ; \(\angle PMA= 90^0\) ; In \(\triangle AMP,\) \(\therefore MA = 8 cm\); Again, BQ = 10 cm. ; NQ = 8 cm; \(\angle BNQ = 90^0\) ; So BN = 6 cm ; Ab = AC + CB = AM + BN = (8 + 6) = 14 cm.
, Avg: 02:04 , 50%✓ SSC CGL 2020141)AB is a diameter of a circle with centre O. The tangent at a point C on the circle meets AB produced at Q. If \(\angle CAB=42^0\), then what is the measure of \(\angle CQA\)?
\(6^0\)
\(\angle OAC = \angle OCA = 42^0 ( \because OA = OC)\); \(\angle OCQ = 90^0 \) (since CQ is tangent). Now in \(\triangle ACQ\), \(\angle A+\angle C+\angle Q =180^0\); ⇒ \(42^0+(42^0+90^0)+x = 180\); x = \(6^0\)
, Avg: 02:31 , 50%✓ SSC CGL 2020142)PAQ is a tangent to circle with centre O, at a point A on it. AB is a chord such that \(\angle BAQ=x^0 (x<90)\). C is a point on the major arc AB such that \(\angle ACB = y^0\). If \(\angle ABO = 32^0\), then the value of x + y is:
116
OA = OB; \(\angle ABO = \angle BAO =32^0\); \(\angle AOB = 116^0\); so \(y ={ 1\over2}\angle AOB = 58^0\); and \(x= 90^0-32^0= 58^0\); x + y = \(58^0 +58^0 = 116^0\)
, Avg: 03:42 , 100%✓ SSC CGL 2020143)In a circle, AB is a the diameter and CD is a chord. AB and CD produced meet at a point P, outside the circle. If PD = 15.3 cm, CD = 11.9 cm and AP = 30.6 cm,then the radius of the circle is is:
8.5 cm
From the property,
\(PA \times PB = PC \times PD\);
\(30.6 \times PB = (PD + CD) \times 15.3\);
\(30.6 \times PB = (15.3 + 11.9) \times 15.3\);
\(30.6 \times PB = 27.2 \times 15.3\);
PB = 416.16/30.6 = 13.6 cm;
Diameter (AB) = PA - PB = 30.6 - 13.6 = 17 cm;
Radius = AB/2 = 17/2 = 8.5 cm
, Avg: 00:39 , 100%✓ SSC CGL 2020144)From an external point P, a tangent PQ is drawn to a circle, with the centre O, touching the circle at Q. If the distance of P from the centre is 13 cm and length of the tangent PQ is 12 cm, then the radius of the circle is:
5 cm
\triangle OPQ is a right angle triangle because \(\angle Q = 90^0\),
By Pythagoras,
\((OQ)^2 + (PQ)^2 = (OP)^2\);
\((OQ)^2 = (13)^2 - (12)^2\);
\((OQ)^2\) = 169 - 144;
\((OQ)^2\) = 25;
OQ = 5 cm.
, Avg: 01:26 , 66%✓ SSC CGL 2020145)In a circle, chords PQ and TS are produced to meet at R. If RQ = 14.4 cm, PQ = 11.2 cm, and SR = 12.8 cm, then the length of chord TS is:
16 cm
RQ X PR = RS X TR; 14.4 X (14.4+11.2) = 12.8 X TR; TR = \({14.4\times25.6\over12.8}=28.8 cm\) ; TS = TR - SR = (28.8 - 12.8) cm = 16 cm
, Avg: 02:27 , 100%✓ SSC CGL 2019146)In a circle, AB and DC are two chords. When AB and DC are produced, they meet at P. If PC = 5.6 cm, PB = 6.3 cm and AB = 7.7 cm, then the length of CD is:
10.15 cm.
, Avg: 02:59 , 100%✓ SSC CGL 2019147)In circle with centre O, AC and BD are two chords. AC and BD meet at E when produced. If AB is the diameter and \(\angle AEB=68^0\), then the measure of \(\angle DOC\) is :
\(44^0\)
, Avg: 02:13 , 100%✓ SSC CGL 2019148)A circle touches the side BC of \(\triangle ABC\) at D and AB and AC are produced to E and F, respectively. If AB = 10 cm, AC = 8.6 cm and BC =6.4 cm, then BE =?
2.5 cm
, Avg: 01:48 , 100%✓ SSC CGL 2019149)Two parallel chords on the same side of the centre of a circle are 12 cm and 20 cm long and the radius of the circle is \(5\sqrt{13}cm\). What is the distance (in cm) between the chords?
2
, Avg: 00:48 , 100%✓ SSC CGL 2019150)Chord AB of a circle is produced to a point P, and is a point on the circle such that PC is a tangent to the circle. If PC = 18 cm, and BP = 15 cm, then AB is equal to:
6.6 cm
By the property,
\(PC^2 = PA \times PB;\)
\((18)^2 = PA \times 15;\)
PA = 324/15 = 21.6 cm;
AB = PA - PB = 21.6 - 15 = 6.6 cm
Class 10 Maths151)If angle of sector is 60°, radius is 3.5 cm then length of the arc is
3.66 cm
, Avg: 00:57 , 90%✓ SSC CGL 2020152)In the figure, PA is a tangent from an external point P to the circle with centre O. If \(\angle POB = 110 ^{\circ}\), then measure of \(\angle APO\) is:
\(20 ^{\circ}\)
PA is a tangent
\(\angle POA =180^{\circ}- 110 ^{\circ}=70^{\circ}\)
\(\angle PAO =90^{\circ}\)
\(\angle APO =180^{\circ}- 70 ^{\circ}-90^{\circ}=20^{\circ}\)