21)

Two chords AB and CD of a circle with centre O intersect each other at P. If \(\angle APC = 95^0\) and \(\angle AOD = 110^0\) , then \(\angle BOC\) is:

SSC CGL 2020

A)

\(70^0\)

B)

\(60^0\)

C)

\(65^0\)

D)

\(55^0\)

Correct Option: B

\(60^0\)

---

For an equal arc, angle at the centre = 2 \(\times\) angle at the circumference  ;  

\(\therefore \angle AOD =2\angle ABD\); ⇒ \(\angle ABD = {110^0\over2}= 55^0= \angle PBD\) ;  

\(\angle APC = \angle BPD = 95^0\);   

In \(\triangle PBD\), \(\angle BPD +\angle PDB+\angle PBD = 180^0\) ;  ⇒ \(\angle BDP= 180-95-55= 30^0\) ;  

\(\therefore \angle BOC = 2\times \angle BDP = 2\times 30= 60^0\)

22)

Chord AB and diameter CD of a circle meet at the point P, outside the circle when the produced, If PB = 8 cm, AB = 12 cm and distance of P from the centre of the circle is 18 cm, the radius (in cm) of the circle is closest to:

SSC CHSL 2021

A)

12

B)

12.8

C)

12.4

D)

13

23)

In a circle with centre O, a 6 cm long chord is at a distance 4 cm from the centre. Find the length of the diameter.

SSC CHSL 2021

A)

5 cm

B)

10 cm

C)

14 cm

D)

7 cm

24)

AB and AC are tangents to a circle with centre O from an external point A. The tangents AB and AC touch the circle at B and C, respectively, such that ∠BAC = 118°. Find the measures of ∠OCB.

SSC CHSL 2021

A)

59° 

B)

62°

C)

60°

D)

54°

25)

Let O be the centre of a circle. PA and PB are tangents to the circle from a point P outside the circle and A and B are points on the circle. If angle APB = 50°, then angle OAB is equal to:

SSC CHSL 2021

A)

25° 

B)

40°

C)

50°

D)

20°

26)

AB and CD are two chords of a circle that intersects at E inside the circle. If ∠BEC = 125° and ∠EBD = 28°, then what is the measure of ∠BAC?

SSC CHSL 2021

A)

87°

B)

55°

C)

56°

D)

97°

27)

P, Q and R are three points on the circumference of a circle such that QR is a diameter and PQ = PR. If the radius of the circle is 7 cm. then the length of PQ is:

SSC CHSL 2021

A)

7 cm

B)

14√2 cm

C)

7√2 cm

D)

7√3 cm

28)

AB is a diameter of a circle with centre O. If C is any point on the circle such that ∠BAC = 42°, then find the measure of ∠BOC.

SSC CHSL 2021

A)

84°

B)

42°

C)

60°

D)

63°

29)

AB is a diameter of the circle with centre 0. The tangent at the point C on the circle meets AB produced at Q. If ∠BAC = 34°, then the measures of ∠CQA (in degrees) will be:

SSC CHSL 2021

A)

22

B)

24

C)

36

D)

26

30)

A and B are two points on a circle with centre O. C is a point on the minor arc of the circle between points A and B. The tangents to the circle at A and B meet each other at a point D. If ∠ ADB = 25°, then ∠ ACB (in degrees) is equal to :

SSC CHSL 2021

A)

102.5

B)

105

C)

100.5

D)

100