Geometry (Part-4)

Total Questions: 50

21. From a point T, the length of the tangent to a circle is 32 cm and the distance of T from the centre is 40 cm. The diameter (in cm) of the circle is: [SSC CGL 12/09/2024 (2nd Shift)]

Correct Answer: (d) 48
Solution:

22. A pair of straight lines from an external point F intersects a circle at A and B (FA < FB) and touches the circle at C. O is the centre of the circle. Given that ∠ACF = 50º and ∠AFC = 30º find ∠AOB. [SSC CGL 12/09/2024 (3rd Shift)]

Correct Answer: (c) 100°
Solution:

23. If ∆PQR ≅ ∆ABC, AB = 6cm ∠B = 50º and ∠A = 70º, then which of the following is true? [SSC CGL 13/09/2024 (1st Shift)]

Correct Answer: (d) QP = 6cm, ∠R = 60º
Solution:

24. A circle's centre is connected to its 50 cm long chord by a perpendicular that is 21 cm long. Find the circle's radius. [SSC CGL 13/09/2024 (2nd Shift)]

Correct Answer: (d)
Solution:

25. ABC is an equilateral triangle. P, Q and R are the mid-points of sides AB, BC and CA, respectively. If the length of the side of the triangle ABC is 11 cm, then the area (in cm²) of ∆PQR is: [SSC CGL 13/09/2024 (2nd Shift)]

Correct Answer: (c)
Solution:

26. P and Q are two fixed points 10 cm apart, and R is a point on PQ such that PR = 6 cm. By what percentage is the length of QR decreased when the length of PR is increased by 5% ? [SSC CGL 13/09/2024 (2nd Shift)]

Correct Answer: (b) 7.5%
Solution:

27. Two circles, centred at P and Q intersect at two points C and D. AB is tangent to the two circles at A and B. If ∠ADB = 68º, then ∠ACB = ________ . [SSC CGL 13/09/2024 (3rd Shift)]

Correct Answer: (b) 112°
Solution:

28. The perimeters of two similar triangles ∆RST and ∆ABC are 26 cm and 39 cm, respectively. If AB = 24cm, then RS is _________. [SSC CGL 13/09/2024 (3rd Shift)]

Correct Answer: (a) 16 cm
Solution:

29. In the following sets, which set represents the angles of a triangle ? [SSC CGL 13/09/2024 (3rd Shift)]

Correct Answer: (a) {30°, 60°, 90°}
Solution:

30. What is the difference in area (in cm²) of ∆ABC having sides of 10 cm, 20 cm and 20 cm, and a right angled triangle ∆PQR with hypotenuse of 13 cm and one of the perpendiculars of 12 cm? [SSC CGL 17/09/2024 (1st Shift)]

Note: √2 = 1.41, √3 = 1.73, √7 = 2.65, √13 = 3.61, √15 = 3.87, √21 = 4.58

Correct Answer: (c) 66.75
Solution: