31)

AB is a chord of a circle with centre O and P is any point on the circle. If  ∠APB = 112°, then what is the measure of ∠OAB ?

SSC CHSL 2021

A)

30°

B)

32°

C)

22°

D)

44°

32)

Two concentric circles are of radii 15 cm and 6 cm. What is the length (in cm) of the chord of the larger circle that is tangent to the smaller circle?

SSC CHSL 2021

A)

4√21

B)

9√21

C)

6√21

D)

3√21

33)

Chords AB and CD of a circle are produced to meet at the point P, outside the circle, and AD is the diameter of the circle. If ∠DAP = 36° and ∠APC = 30°, then what will be the measure of ∠CBD?

SSC CHSL 2021

A)

34°

B)

26°

C)

24°

D)

16°

34)

A chord PQ of a circle C₁ of radius 9.25 cm touches another circle C₂ that is concentric to C₁, and the radius of C₂ is 3 cm. What is the length (in cm) of PQ?

SSC CHSL 2021

A)

12

B)

19.5

C)

17.5

D)

15

35)

In a circle, AB and DC are two chords. When AB and DC are produced, they meet at P. If PC = 2.8 cm, PB = 3.15 cm and AB = 3.85 cm, then CD = ?

SSC CHSL 2021

A)

6.975 cm

B)

5.075 cm

C)

4.175 cm

D)

7.875 cm

36)

If PA and PB are tangents drawn to a circle with centre O at A and B from external point P such that ∠APB = 78°, then ∠OAB is equal to:

SSC CHSL 2021

A)

39°

B)

29°

C)

12°

D)

36°

37)

A circle is inscribed in a triangle ABC. It touches sides AB, BC and AC at points R, P and Q, respectively. If AQ = 6.5 cm, PC = 7.5 cm and BR = 9 cm, then the perimeter (in cm) of the triangle ABC will be:

SSC CHSL 2021

A)

27.5

B)

46

C)

55

D)

23

38)

Two circles of radii 4 cm and 3 cm, respectively, touch each other externally. What is the distance (in cm) between their centres?

SSC CHSL 2021

A)

16

B)

7

C)

5

D)

9

39)

The distance between two equal parallel chords of a circle is 10 cm. If the chords are 24 cm long, then what is the length of the radius?

SSC CHSL 2021

A)

26 cm

B)

13 cm

C)

2√61 cm

D)

17 cm

40)

Two chords PQ and RS of a circle meet at A when produced. AT is a tangent to the circle meeting it at T. The ratio PA : SA is equal to which of the following?

SSC CHSL 2021

A)

AQ : AT

B)

RQ : QT

C)

RA : AQ

D)

AQ : QR