**Assertion and Reason Questions for Class 9 Maths Chapter 10 Circles**

** Directions: **Choose the correct answer out of the following choices :

(a) Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.

(b) Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.

(c) Assertion is correct statement but Reason is wrong statement.

(d) Assertion is wrong statement but Reason is correct statement.

Q.1. Assertion : In the given figure, ∠ABC = 70° and ∠ACB = 30°. Then, ∠BDC = 80°.

Reason : Angles in the same segment of a circle are equal.

## Answer

Answer: (a)Q.2. Assertion : In the given figure, O is the centre of circle. If ∠AOC = 140°, then ∠ABC =110°.

Reason : In cyclic quadrilateral, opposite angles are supplementary.

## Answer

Answer: (a)Q.3. Assertion : In the given figure, ∠BAO = 30° and ∠BCO = 40°. Then the measure of ∠AOC= 60°.

Reason : Angle subtended by an arc of a circle at the centre of the circle is twice the angle subtended by that arc on the remaining part of the circle.

## Answer

Answer: (d)Q.4. Assertion : AB and CD are two parallel chords of a circle whose diameter is AC. Then AB ≠ CD.

Reason : Perpendicular from the centre of a circle bisects the chord.

## Answer

Answer: (d)Q.5. Assertion : In the given figure, O is the centre of the circle of radius 5 cm. If OP ⊥ AB, OQ ⊥ CD, AB || CD, AB = 6 cm and CD = 8 cm, then PQ = 6 cm.

Reason : Perpendicular bisectors of two chords of a circle intersect at its centre.

## Answer

Answer: (d)Q.6. Assertion : The length of a chord which is at a distance of 5 cm from the centre of a circle of radius 10 cm is 17.32 cm.

Reason : The perpendicular from the centre of a circle to a chord bisects the chord.

## Answer

Answer: (a)Q.7. Assertion : In the given figure, ABCD is a cyclic quadrilateral in which AB is extended to F and BE || DC. If ∠FBE = 20° and ∠DAB = 95°, then ∠ADC = 105°.

Reason : A line drawn through the centre of a circle to bisect a chord is perpendicular to the

chord.