11)

Chords AB and CD of a circle, when produced, meet at the point P. If AB = 6.3 cm, BP = 4.5 cm, and CD = 3.6 cm, then the length (in cm) of PD is

SSC CGL 2022

A)

3.5 cm

B)

5.4 cm

C)

4.8 cm

D)

3.1 cm

12)

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

SSC CGL 2022

A)

3

B)

10

C)

8

D)

5

13)

In the given figure, O is the centre of the circle. ∠POQ = 54°. What is the measure (in degree) of ∠PRQ?

SSC CGL 2022

A)

235

B)

137

C)

153

D)

207

14)

An isosceles ΔMNP is inscribed in a circle. If MN = MP = 16√5 cm, and NP = 32 cm, what is the radius (in cm) of the circle?

SSC CGL 2022

A)

18√5

B)

20√5

C)

18

D)

20

15)

In the following figure, P and Q are centers of two circles. The circles are intersecting at points A and B. PA produced on both the sides meets the circles at C and D. If ∠CPB = 100°, then find the value of x.

SSC CGL 2022

A)

115

B)

100

C)

110

D)

120

16)

AB is a chord of a circle with centre O, while PAQ is the tangent at A.R is a point on the minor arc AB. If ∠BAQ = 70° then find the measure of ∠ARB .

SSC CGL 2022

A)

70°

B)

125°

C)

110°

D)

145°

17)

A circle with centre O has radius 15 cm. D is a point on the circle such that a 24 cm long chord AB is bisected by OD at point C. Find the length of CD (in cm).

SSC CGL 2022

A)

4

B)

6

C)

9

D)

10

18)

AB is a diameter of a circle with centre O. The tangent at a point C on the circle and AB, when produced, meet at the point P. If ∠APC = 38^∘, then what is the measure of ∠PCB?

SSC CGL 2022

A)

29°

B)

26°

C)

23°

D)

19°

19)

PQ and RS are two parallel chords of a circle of length 14 cm and 48 cm, respectively, and lie on the same side of the centre O. If the distance between the chords is 17 cm, what is the radius (in cm) of the circle?

SSC CGL 2022

A)

20

B)

25

C)

28

D)

24

20)

In the following figure, MN is a tangent to a circle with centre O at point A. If BC is a diameter and ∠ABC = 42°, then find the measure of ∠MAB.

SSC CGL 2022

A)

84

B)

42

C)

45

D)

48