Circles Quiz

In the following figure, O is the centre of the circle. If ∠BAC = 60°, then what its the value of OBC?

1. 60o
2. 50o
3. 30o
4. 120o

Answer: (c) 30o

A, B, C and D are points on the circumference of the circle, centre O. DOB is a straight line and angle DAC = 58o. Find the value of ∠CDB.

1. 45o
2. 30o
3. 15o
4. 24o

Answer: (d) 24o

In the given figure, O is the centre of the circle with chords AP and BP being produced to R and Q respectively. If ∠QPR = 35°, find the measure of ∠AOB.

1. 55o
2. 70o
3. 100o
4. 50o

Answer: (b) 70o

In the following figure, O is the centre of the circle, AC is the diameter and if ∠APB = 120°, then find the angle ∠BQC.

1. 30o
2. 150o
3. 90o
4. 120o

Answer: (b) 150o

The distance between two parallel chords of length 24 cm and 10 cm is L. If the radius of the circle is 13 cm, find the value of L?

1. 12 cm
2. 10 cm
3. 15 cm
4. 17 cm

Answer: (d) 17 cm

In a circle with centre O, AB and CD are parallel chords on the opposite sides of a diameter. If AB = 12 cm, CD = 18 cm and the distance between the chords AB and CD is 15 cm, then find the radius of the circle (in cm).

1. 12.5 cm
2. 10.8 cm
3. 11.5 cm
4. 13.5 cm

Answer: (b) 10.8 cm

The vertices of a ∆ABC lie on a circle with centre O. AO is produced to meet the circle at the point P. D is a point on BC such that AD ⊥ BC. If ∠B = 68° and ∠C = 52°, then what is the value of the measure of ∠DAP?

1. 25o
2. 45o
3. 16o
4. 20o

Answer: (c) 16o

In the given figure, the angles ∠ADE and ∠ABC differ by 15°. Find the value of ∠CAE.

1. 10o
2. 7.5o
3. 15o
4. 30o

Answer: (c) 15o

In the given figure, P, Q, R and S are concyclic points, and O is the mid-point of the diameter QS. If ∠QPR = 25°, then find the value of ∠SOR.

1. 130o
2. 120o
3. 75o
4. 100o

Answer: (a) 130o

In the following figure, O is the centre of the circle and CD = DE = EF = GF. If ∠COD = 40°, then find reflex ∠COG.

1. 200o
2. 190o
3. 280o
4. 160o

Answer: (a) 200o