1)

A circle is inscribed in a triangle ABC. It touches sides AB, BC and AC at points R, P and Q, respectively. If AQ = 3.5 cm, PC = 4.5 cm and BR = 7 cm, then the perimeter (in cm) of the triangle ΔABC is:

SSC CPO 2020

A)

45

B)

15

C)

28

D)

30

2)

PA and PB are two tangents from a point P outside the circle with centre O. If A and B are points on the circle such that ∠APB = 128°, then ∠OAB is equal to:

SSC CPO 2020

A)

38°

B)

64°

C)

72°

D)

52°

3)

In a ΔABC, the bisectors of ∠B and ∠C meet at O. If ∠BOC = 142°, then the measure of ∠A is:

SSC CPO 2020

A)

52°

B)

68°

C)

116°

D)

104°

4)

PA and PB are two tangents from a point P outside the circle with centre O. If A and B are points on the circle such that∠APB = 100°, then∠OAB is equal to:

SSC CPO 2020

A)

45°

B)

70°

C)

50°

D)

35°

5)

PA and PB are two tangents from a point P outside the circle with center O at the point A and B on it. If ∠APB = 130°, then ∠OAB is equal to:

SSC CPO 2020

A)

45°

B)

65°

C)

35°

D)

50°

6)

Chord AB of a circle is produced to a point P, and C is a point on the circle such that PC is a tangent to the circle. If PC = 12 cm, and BP = 10 cm, then the length of AB (in cm) is:

SSC CPO 2020

A)

4.4

B)

6

C)

5

D)

5.4

7)

PA and PB are two tangents from a point P outside the circle with centre O. If A and B are points on the circle such that ∠APB = 142°, then ∠OAB is equal to:

SSC CPO 2020

A)

58°

B)

64°

C)

31°

D)

71°

8)

In a circle with centre O, AD is a diameter and AC is a chord. Point B is on AC such that OB = 7 cm and ∠OBA = 60°, If ∠DOC = 60°, then what is the length of BC?

SSC CPO 2020

A)

7 cm

B)

\(3\sqrt 7\) cm

C)

3.5 cm

D)

\(5\sqrt 7\) cm

9)

The circles of radii 15 cm and 10 cm intersect each other and the length of their common chord is 16 cm. What is the distance (in cm) between their centres?

SSC CPO 2020

A)

\(6 + \sqrt {161}\)

B)

\(15 + 2\sqrt {161}\)

C)

\(12 + 3\sqrt 7\)

D)

\(10 + \sqrt {161}\)