Geometry

Total Questions: 50

11. In a triangle PQR, RS intersects PQ at point S. The sides of the triangle QR = 36 cm, SQ = 27 cm, RS = 18 cm and ∠QRS = ∠QPR. What is the ratio of the perimeter of △PRS to that of QSR? [SSC CHSL 10/07/2024 (3rd Shift)]

Correct Answer: (b) 7/9
Solution:

12. Solve it- [SSC CHSL 09/07/2024 (4th Shift)]

I) △ACG ≅ △BEH
II) △CDE ≅ △DEB ≅ △DCA
III) △HFB ≅ △AFG

Correct Answer: (d) I and II
Solution:

13. ABC is a right-angled triangle, right angled at A in such a way that AB = AC and the bisector of angle B intersects the side AC at D. DM is perpendicular to BC, intersecting BC at M. If AB = 12 cm and BC = 12√2 cm, then find the length of side AD. [SSC CHSL 08/07/2024 (2nd Shift)]

Correct Answer: (b)
Solution:

14. Two circles with centres M and N have radii 5 cm and 8 cm, respectively. The circles touch each other externally at point T. A line PR is drawn such that the points M, T and N lie on PR, P being closer to M. From P, a tangent PQ = 12 cm is drawn to the circle with centre M touching at Q, and from R, another tangent RS = 15 cm is drawn to the circle with centre N touching at S. What is the length (in cm) of PR ? [SSC CHSL 04/07/2024 (3rd Shift)]

Correct Answer: (b) 43
Solution:

15. Two circles of radius 7 units each, intersect in such a way that the common chord is of length 7 units. What is the common area in square units of the intersection? [SSC CHSL 01/07/2024 (4th Shift)]

Correct Answer: (d)
Solution:

16. In a circle, ABCD is a cyclic quadrilateral in which AE is drawn parallel to CD, and BA is produced to F. If ∠ABC = 85º and ∠FAE = 24º find the value of ∠BCD. [SSC CHSL 01/07/2024 (2nd Shift)]

Correct Answer: (a) 119º
Solution:

17. What is the length (in cm) of chord PQ in a circle with a radius of 7 cm, where a diameter AB and non-diameter chord PQ intersect perpendicularly at point C, and the ratio of AC to BC is 4: 3? [SSC CPO 28/06/2024 (2nd Shift)]

Correct Answer: (b) 8√3
Solution:

18. The angles of a triangle are in the ratio 1:2:3, then find the ratio of the corresponding sides. [SSC CPO 28/06/2024 (1st Shift)]

Correct Answer: (d) 1 : √3 : 2
Solution:

19. In ∆ABC, P is a point on AB such that PB:AP = 3:4 and PQ is parallel to AC. If AR and QS are perpendicular to PC and QS = 9 cm, what is the length (in cm) of AR? [SSC CPO 27/06/2024 (1st Shift)]

Correct Answer: (c) 21
Solution:

20. The lengths of the three sides of a triangle are given as 3 cm, 4 cm and 5 cm. The ratio of their corresponding altitudes to the opposite vertices will be: [Graduate Level 26/06/2024 (Shift-3)]

Correct Answer: (c) 20 : 15 : 12
Solution: