Question

In triangle ABC, ∠A = 35° and ∠C = 55°.

Assertion (A): Circle with AC as diameter will pass through the vertex B. 

Reason (R): ∠ABC = 180° − 35° + 55°

= 90°

= angle of semi-circle

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

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

Explanation:

Given, in triangle ABC, ∠A = 35° and ∠C = 55°.

The sum of angles in a triangle is always 180°.

⇒ ∠A + ∠B + ∠C = 180°

⇒ 35° + ∠B + 55° = 180°

⇒ 90° + ∠B = 180°

⇒ ∠B = 180° − 90°

⇒ ∠B = 90°.

An angle inscribed in a semicircle is always a right angle (90°).

So, reason (R) is true.

Since ∠ABC is 90°, and AC is the diameter of the circle, the circle must pass through point B.

This is because the angle subtended by the diameter (AC) at any point on the circumference of the circle (in this case, point B) is always a right angle.

So, assertion (A) is true.

∴ Both A and R are true and R is correct reason for A.