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?

, Avg: 00:53 , 75%✓ 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?

, Avg: 02:15 , 33%✓ 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)?

, Avg: 01:45 , 80%✓ 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:

, Avg: 01:07 , 50%✓ SSC CHSL 2021

A)

8√3 cm

B)

8 cm

C)

8√2 cm

D)

4√3 cm