Question

AB is diameter of the circle and ∠ACD = 38°.

Assertion (A): x = 38°.

Reason (R): ∠ACB = 90°
x = ∠DCB
=  90° − 38 = 52°

Options

• A is true, R is false.

• A is false, R is true.

• Both A and R are true and R is the correct reason for A.

• Both A and R are true and R is the incorrect reason for A.

Answer 1

A is false, R is true.

Explanation:

Join DB and CB.

It is given AB is diameter of the circle and angles in a semicircle is a right angle.

⇒ ∠ACB = 90°

⇒ ∠ACD + ∠DCB = 90°

⇒ 38° + ∠DCB = 90°

⇒ ∠DCB = 90° − 38°

⇒ ∠DCB = 52°

We know that, angles subtended by the same chord in the same segment of a circle are equal.

⇒ ∠BAD (x) = ∠BCD = 52°

So, assertion (A) is false but reason (R) is true.