Question

In the given figure, AT is tangent to a circle centred at O. If ∠CAT = 40°, then ∠CBA is equal to ______. 

Options

• 70°

• 50°

• 65°

• 40° 

Answer 1

In the given figure, AT is tangent to a circle centred at O. If ∠CAT = 40°, then ∠CBA is equal to 40°.

Explanation:

Given

∠CAT = 40°

Find ∠CBA

∠BAT = 90°

⇒ ∠BAC + ∠CAT = 90°

⇒ ∠BAC = 50°

⇒ ∠ACB = 90°       ...[Angle in semi-circle]

In ΔABC

∠A + ∠B + ∠C = 180°

50° + ∠B + 90° = 180°

∠B = 180° − 140°

∠B = 40°