51)

O is the centre of a circle of radius 9 cm. M is a point outside the circle and MN is a tangent to the circle. What is the length (in cm) of OM if the length MN is 12 cm?

SSC CHSL 2021

A)

15

B)

21

C)

12

D)

17

52)

ΔABC is drawn in a circle such that AC = BC and ∠BAC = 65°. From points B and C two tangents are drawn which intersect at point P. What is the measure of ∠BPC?

SSC CHSL 2021

A)

52.5°

B)

32.5°

C)

50°

D)

55°

53)

Two circles with centres O and P and radii 17 cm and 10 cm, respectively, intersect each other at A and B. The length of the common chord AB is 16 cm. What is the perimeter of the triangle OAP (in cm)?

SSC CHSL 2021

A)

40

B)

48

C)

25

D)

33

54)

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

SSC CHSL 2021

A)

8√3 cm

B)

8 cm

C)

8√2 cm

D)

4√3 cm