111)

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°

112)

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

113)

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)

\(10 + \sqrt {161}\)

114)

AB is a diameter of a circle with centre O. A tangent is drawn at point A. C is a point on the circle such that BC produced meets the tangent at P. If ∠APC = 62º, then find the measure of the minor arc AC.

SSC CGL 2022

A)

31º

B)

62º

C)

28º

D)

56º

115)

O is the centre of a circle with diameter 20 cm. T is a point outside the circle and TA is a tangent to a circle. If OT is 26 cm, what is the length (in cm) of the tangent TA?

SSC CGL 2022

A)

24

B)

20

C)

18

D)

26

116)

In a circle with centre O, chords PR and QS meet at the point T, when produced, and PQ is a diameter. If ∠ROS = 42º, then the measure of ∠PTQ is

SSC CGL 2022

A)

69º

B)

59º

C)

58º

D)

48º

117)

Two circles touch each other externally at T. RS is a direct common tangent to the two circles touching the circles at P and Q. ∠TPQ = 42°. ∠PQT (in degrees) is:

SSC CGL 2022

A)

45

B)

48

C)

42

D)

60

118)

AB is the diameter of a circle with centre O. C and D are two points on the circumference of the circle on either side of AB, such that ∠CAB = 42° and ∠ABD = 57°. What is difference (in degrees) between the measures of ∠CAD and ∠CBD?

SSC CGL 2022

A)

30°

B)

25°

C)

35°

D)

18°

119)

A tangent is drawn from a point P to a circle, which meets the circle at T such that PT = 10.5 cm. A secant PAB intersects the circle in points A and B. If PA = 7 cm, what is the length (in cm) of the chord AB?

SSC CGL 2022

A)

8.75

B)

8.5

C)

7.75

D)

8.45

120)

Two common tangents AC and BD touch two equal circles each of radius 7 cm, at points A, C, B and D, respectively, as shown in the figure. If the length of BD is 48 cm, what is the length of AC?

SSC CGL 2022

A)

48 cm

B)

40 cm

C)

50 cm

D)

30 cm