Geometry (Part-12)

Total Questions: 50

31. In ∆PQR, PQ = PR and S is a point on QR such that ∠PSQ = 96° + ∠QPS and ∠QPR = 132º. What is the measure of ∠PSR? [SSC CGL Tier II (03/02/2022)]

Correct Answer: (c) 54°
Solution:

32. In ∆АВС, ∠BAC = 90º, AD is drawn perpendicular from A on BC. Which among the following is the mean proportional between BD and BC? [SSC MTS 05/10/2021 (Morning)]

Correct Answer: (b) AB
Solution:

33. In a triangle ABC AB : AC = 5:2 BC = 9 cm. BA is produced to D, and the bisector of the Angle CAD meets BC produced at E. What is the length (in cm) of CE? [SSC CGL 13/08/2021 (Afternoon)]

Correct Answer: (c) 6
Solution:

34. In a circle with centre O, AD is diameter and AC is chord. Point B is on AC such that OB = 7cm and ∠OBA = 60º. If ∠DOC = 60º, then what is the length of BC (in cm)? [SSC CGL 13/08/2021 (Afternoon)]

Correct Answer: (a) 7
Solution:

35. In ∆ABC, ∠C = 90º and Q is the midpoint of BC. If AB = 10 cm and AC = 2√10 cm, then the length of AQ is: [SSC CGL 13/08/2021 (Evening)]

Correct Answer: (a) √55 cm
Solution:

36. In a circle with centre O and radius 5 cm. AB and CD are two parallel chords of lengths 6 cm and x cm, respectively and the chords are on the opposite side of the centre O. The distance between the chords is 7 cm. Find the value of x ? [SSC CGL 16/08/2021 (Morning)]

Correct Answer: (b) 8
Solution:

37. In a circle with center O, AB is a diameter and CD is a chord such that ∠ABC 34° and CD = BD. What is the measure of ∠DBC? [SSC CGL 16/08/2021 (Morning)]

Correct Answer: (d) 28°
Solution:

38. ΔΑΒC is inscribed in a circle with center O, such that ∠ACB = 115°, O is joined to A. What is the measure of ∠OAB? [SSC CGL 16/08/2021 (Evening)]

Correct Answer: (c) 25°
Solution:

39. A triangle ABC has sides 5 cm, 6 cm and 7 cm. AB extends touches a circle at P and AC extended touches the same circle at Q. Find the length (in cm) of AQ. [SSC CGL 17/08/2021 (Morning)]

Correct Answer: (c) 9
Solution:

40. Points A and B are on a circle with center O. PAM and PBN are tangents to the circle at A and B respectively from a point P outside the circle. Point Q is on the major arc AB such that ∠QAM = 58° and QBN = 50°, then find the measure of ∠APB. [SSC CGL 17/08/2021 (Evening)]

Correct Answer: (c) 36°
Solution: