Geometry (Part-11)

Total Questions: 50

41. AB is a diameter of a circle with centre O. A tangent is drawn at point A. C is a point on the circle such that BC produced meets the tangent at P. If ∠APC = 62°, then find the measure of angle subtended by the minor arc AC. [SSC CGL 11/04/2022 (Morning)]

Correct Answer: (c) 28°
Solution:

The tangent is perpendicular to the diamete.
∠A = 90º
Now ∠ABP + ∠APB = 90º
∠ABP + 62º = 90º ⇒ ∠ABP = 28º

42. In a ∆ABC, points P, Q and R are taken on AB, BC and CA, respectively, such that BQ = PQ and QC = QR. If ∠BAC = 75°, what is the measure of ∠PQR (in degrees)? [SSC CGL 11/04/2022 (Morning)]

Correct Answer: (b) 30
Solution:

43. An equilateral triangle ABC is inscribed in a circle with centre O. D is a point on the minor arc BC and ∠CBD = 40°. Find the measure of ∠BCD. [SSC CGL 11/04/2022 (Morning)]

Correct Answer: (c) 20°
Solution:

44. 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 is the measure of the lengths(in cm) of AE and BC ? [SSC CGL 11/04/2022 (Evening)]

Correct Answer: (a) 4 , 2.5
Solution:

45. AB is the diameter of a circle with center O, C and D are two points on the circumference of the circle on either side of AB such that ∠CAB = 42° and ∠ABD = 57°. What is the measure of ∠CAD and ∠CBD? [SSC CGL 11/04/2022 (Evening)]

Correct Answer: (b) 75 and 105
Solution:

46. A cyclic quadrilateral ABCD is drawn in a circle with centre O. A and C are joined to O. If ∠ABC = 2p and ∠ADC = 3p, what is the measure (in degrees) of the ∠AOC reflex? [SSC CGL 12/04/2022 (Afternoon)]

Correct Answer: (d) 216
Solution:

47. In a circle with centre O, AC and BD are two chords. AC and BD meet at E, when produced. If AB is a diameter and ∠AEB = 36º then the measure of ∠DOC is: [SSC CGL 12/04/2022 (Evening)]

Correct Answer: (d) 108°
Solution:

48. In a circle of diameter 20 cm, chords AB and CD are parallel to each other. BC is diameter. If AB is 6 cm from the centre of the circle, what is the length (in cm) of the chord CD ? [SSC CGL 13/04/2022 (Morning)]

Correct Answer: (d) 16
Solution:

49. In the given figure, O is the centre of the circle. ∠POQ = 54º. What is the measure (in degree) of ∠PRQ ? [SSC CGL 13/04/2022 (Afternoon)]

Correct Answer: (d) 153
Solution:

50. Explain it- [SSC CGL 13/04/2022 (Evening)]

Correct Answer: (c) 26
Solution: