Question

In the given figure, two circles touch each other at C and AB is a tangent to both the circles. The measure of ∠ACB is ______.

Options

• 45°

• 60°

• 90°

• 120°

Answer 1

In the given figure, two circles touch each other at C and AB is a tangent to both the circles. The measure of ∠ACB is 90°.

Explanation:

Draw a tangent to the circles at point C. Let it meet AB at P.

Then, PA = PC and PB = PC.

PA = PC ⇒ ∠PAC = ∠PCA

PB = PC ⇒ ∠PBC = ∠PCB

∴ ∠PAC + ∠PBC = ∠PCA + ∠PCB = ∠AСВ

⇒ ∠PAC + ∠PBC + ∠ACB = 2∠ACB

⇒ 180° = 2∠ACB

⇒ ∠AСB = 90°