31)

In a circle with centre O, PQ, and QR are two chords such that ∠PQR = 118°. What is the measure of ∠OPR?

SSC CGL 2022

A)

31°

B)

36°

C)

28°

D)

26°

32)

AB is the diameter of a circle with centre O. C and D are two points on the circle on either side of AB, such that ∠CAB = 52° and ∠ABD = 47°. What is the difference (in degrees) between the measures of ∠CAD and ∠CBD?

SSC CGL 2022

A)

10

B)

15

C)

25

D)

20

33)

AB and CD are two chords in a circle with centre O and AD is the diameter. When produced, AB and CD meet at the point P. If ∠DAP = 27°, ∠APD = 35°, then what is the measure (in degrees) of ∠DBC?

SSC CGL 2022

A)

26

B)

30

C)

32

D)

28

34)

Two circles touch each other externally at P. AB is a direct common tangent to the two circles, A and B are points of contact, and ∠PAB = 40° . The measure of ∠ABP is:

SSC CGL 2022

A)

50°

B)

55°

C)

45°

D)

40°

35)

The circumference of the two circles is 198 cm and 352 cm respectively. What is the difference between their radii?

SSC CGL 2022

A)

49.5 cm

B)

16.5 cm

C)

45 cm

D)

24.5 cm

36)

Radius of a circle is 10 cm. Angle made by chord AB at the centre of this circle is 60 degree. What is the length of this chord?

SSC CGL 2022

A)

30 cm

B)

20 cm

C)

40 cm

D)

10 cm

37)

O is the centre of this circle. Tangent drawn from a point P, touches the circle at Q. If PQ = 24 cm and OQ = 10 cm, then what is the value of OP?

SSC CGL 2022

A)

13 cm

B)

52 cm

C)

26 cm

D)

15 cm

38)

Two equal circles of radius 8 cm intersect each other in such a way that each passes through the centre of the other. The length of the common chord is:

SSC CGL 2022

A)

\(2\sqrt3\)

B)

\(\sqrt 3 \)

C)

\(8\sqrt3 cm \)

D)

\(4\sqrt3\)

39)

A chord of length 42 cm is drawn in a circle of diameter 58 cm. Another chord of length 40 cm is drawn parallel to the chord of length 42 cm. Find the difference between the distances of the two chords from the centre.

SSC CGL 2022

A)

3 cm

B)

1 cm

C)

4 cm

D)

2 cm

40)

The length of the chord of a circle is 24 cm, and the perpendicular distance between the centre and the chord is 5 cm. The radius of the circle is:

SSC CGL 2022

A)

12 cm

B)

13 cm

C)

10 cm

D)

24 cm