21)

Chords AB and CD of a circle intersect externally at P. If AB = 7 cm, CD = 1 cm and PD = 5 cm, then 50% of the length of PA (in cm) is:

SSC CGL 2022

A)

8

B)

10

C)

5

D)

3

22)

AB is a chord of a circle with centre O. C is a point on the circumference of the circle in the minor sector. If ∠ABO = 40°, what is the measure (in degree) of ∠ACB?

SSC CGL 2022

A)

130°

B)

120°

C)

110°

D)

100°

23)

In a circle with centre O and of radius 13 cm, two parallel chords are drawn on different sides of the centre. If the length of one chord is 10 cm and the distance between the two chords is 17 cm, then find the difference in lengths of the two chords (in cm).

SSC CGL 2022

A)

12

B)

24

C)

10

D)

14

24)

In a circle with centre O, PA and PB are tangents to the circle at point A and point B, respectively. C is a point on the major arc AB. If ∠ACB = 50°, then find the measure of ∠APB.

SSC CGL 2022

A)

80°

B)

50°

C)

100°

D)

90°

25)

Points A and B are on a circle with centre O. PA and PB are tangents to the circle from an external point P. If PA and PB are inclined to each other at 42°, then find the measure of ∠OAB.

SSC CGL 2022

A)

21°

B)

69°

C)

42°

D)

25°

26)

AB is a chord in the minor segment of a circle with center O. C is a point between A and B on the minor arc AB. The tangents to the circle at A and B meet at the point D. If ∠ACB = 116°, then the measure of ∠ADB is

SSC CGL 2022

A)

56°

B)

52°

C)

64°

D)

48°

27)

AC is the diameter of a circle dividing the circle into two semicircles. ED is a chord in one semicircle, such that ED is parallel to AC. B is a point on the circumference of the circle in the other semicircle. ∠CBE = 75°. What is the measure (in degrees) of ∠CED?

SSC CGL 2022

A)

68°

B)

37°

C)

15°

D)

75°

28)

The radii of two concentric circles with centre O are 26 cm and 16 cm. Chord AB of the larger circle is tangent to the smaller circle at C and AD is a diameter. What is the length of CD?

SSC CGL 2022

A)

35 cm

B)

42 cm

C)

38 cm

D)

36 cm

29)

O is the centre of a circle of radius 10 cm. P is a point outside the circle and PQ is a tangent to the circle. What is the length (in cm) of PQ if the length OP is 26 cm?

SSC CGL 2022

A)

\(2 \sqrt{194}\)

B)

25

C)

24

D)

20

30)

AB is a chord of a circle with centre O. C is point on the circle in the minor sector. If ∠ABO = 50°, then what is the degree measure of ∠ACB ?

SSC CGL 2022

A)

130°

B)

140°

C)

100°

D)

110°