Geometry (Part-5)

Total Questions: 50

31. Which of the following is a correct statement? [SSC CHSL 01/07/2024 (1st Shift)]

Correct Answer: (a) If two circles touch each other, the point of contact lies on the line joining the two centres.
Solution:

Only option (a) is the correct option.
If two circle touch each other, the point of contact lies on the line joining the two centres.

32. PQ is a diameter of a circle with centre O. The tangents at R meets PQ produced at A. If ∠RPQ = 27°, then measure of ∠RQP is: [SSC CHSL 01/07/2024 (2nd Shift)]

Correct Answer: (a) 63°
Solution:

33. Two circles touch each other at a point O. AB is a simple common tangent to both the circles touching at point A and point B. If radii of the circles are 9 cm and 4 cm, then find AB. [SSC CHSL 01/07/2024 (2nd Shift)]

Correct Answer: (b) 12 cm
Solution:

34. In a ∆ABC, two medians AD and BE intersect at G at right angles. If AD = 18 cm and BE = 12 cm, then the length of BD is equal to: [SSC CHSL 01/07/2024 (2nd Shift)]

Correct Answer: (b) 10 cm
Solution:

35. CD is a tangent to a circle of circumference of 88 cm with its centre at O. OC cuts the circle at P while OD cuts circle at V such that ∠COD = 90°. Length of PC is 6 cm. What is half of CD (in cm) if OD exceeds OC by 1 cm? [SSC CHSL 01/07/2024 (3rd Shift)]

Correct Answer: (a) 14.5
Solution:

36. Explain it- [SSC CHSL 01/07/2024 (3rd Shift)]

Correct Answer: (c) 25/3
Solution:

37. Given is a circle with centre at C. A, B and D are the points on the circumference. Find ∠ABC [SSC CHSL 01/07/2024 (4th Shift)]

Correct Answer: (d) 30°
Solution:

38. Diagonals of a trapezium ABCD with AB || DC, intersect each other at the point 'O'. If AB = 2.5CD find the ratio of the area of triangle AOB to the area of triangle COD. [SSC CHSL 01/07/2024 (4th Shift)]

Correct Answer: (b) 25:4
Solution:

39. The areas of two similar triangles ∆PQR and ∆XYZ are 12.96 cm² and 635.04 cm², respectively. If QR = 2.9 cm, then the length (in cm) of YZ equals: [SSC CHSL 02/07/2024 (1st Shift)]

Correct Answer: (d) 20.3
Solution:

40. If ∆ABC and ∆PQR are similar. AB = 8 cm, PQ = 12 cm, QR = 18 cm and RP = 24 cm, then the perimeter of ∆ABC is_______cm. [SSC CHSL 02/07/2024 (2nd Shift)]

Correct Answer: (a) 36
Solution: