Geometry (Part-11)

Total Questions: 50

31. An arc on a circle that is 15 cm long subtends a 24° angle at the centre. What is the circumference of the circle? [SSC CHSL 02/06/2022 (Afternoon)]

Correct Answer: (d) 225 cm
Solution:

32. PQ and RS are two parallel chords of a circle of length 10 cm and 24 cm, respectively, and lie on the same side of the centre O. If the distance between the chords is 7 cm, what is the radius (in cm) of the circle? [SSC CHSL 03/06/2022 (Afternoon)]

Correct Answer: (c) 13
Solution:

33. If the corresponding angles of two triangles are equal and satisfy (PX)/(ER) = (ZX)/(RF) = (PZ)/(EF), then  [SSC CHSL 06/06/2022 (Afternoon)]

Correct Answer: (b) ∆PXZ is similar to ∆ERF
Solution:

34. Given below are some of the measures of the sides and angles of five triangles. Which of the triangles given in the options is not congruent to ∆ABC ? [SSC CHSL 06/06/2022(Evening)]

Correct Answer: (c) ∆JKL
Solution:

On checking the options, we get ∆ABC ≠ ∆JKL
For, ∆ABC to be congruent to ∆JKL we should have, AB = JK = 3.6 cm, BC = LJ = 4cm, ∠A = ∠J = 52.4º but here ∠B = ∠J = 52.4º, which is possible.

35. The area of a right-angled triangle is 42 cm². If the length of one of its two sides containing the right angle is 10 cm, find the length (in cm) of the other side that contain the right angle. [SSC CHSL 06/06/2022 (Evening)]

Correct Answer: (c) 8.4
Solution:

36. ABCD is a square of 21 cm. A circle is inscribed in the square, which touches the sides of the square at P, Q, R, and S as shown below in the figure. What is the area (in cm²) of the non-shaded region? [figure is not drawn to scale and take π = 22/7] [SSC CHSL 07/06/2022 (Afternoon)]

Correct Answer: (d) 94.5
Solution:

37. Calculate the area (in cm²) of the following diagram. [SSC CHSL 07/06/2022 (Afternoon)]

Correct Answer: (a) 45
Solution:

In this figure we can clearly see five square of side 3 cm is formed when a line is produced So, area of shaded region = 5 × 3² = 45cm²

38. Each edge of the following square is 20 cm long, and a circle is inscribed in the square as shown. What is the area of the shaded region (in cm²) ? [Use π = 3.14] [SSC CHSL 08/06/2022 (Afternoon)]

Correct Answer: (c) 86
Solution:

Area of the square = a² = 20² = 400
Radius of circle = half of the side of square = 10 cm
Area of the circle = πr²
= 3.14 × 10 × 10 = 314
Area of shaded region = 400 - 314 = 86 cm²

39. In a circle, AB and CD are two diameters which are perpendicular to each other. Find the length of chord AC. [SSC CHSL 09/06/2022 (Afternoon)]

Correct Answer: (b) AB/√2
Solution:

40. The ratio in which a transverse common tangent is drawn to two circles with radii 4 cm and 6 cm, respectively, divides the line joining their centres is: [SSC CHSL 09/06/2022 (Evening)]

Correct Answer: (a) 2 : 3
Solution: