Question

In the given figure, O is the centre of a circle, BOA is its diameter and the tangent at the point P meets BA extended at T. If ∠PBO = 30° then ∠PТA = ?

विकल्प

• 60°

• 30°

• 15°

• 45°

Answer 1

30°

Explanation:

∠APB = 90°   ...[Angle in a semicircle]

∴ ∠PAB = 90° – ∠PBA

= 90° – 30°

= 60°

∠PAT + ∠РAВ = 180°   ...[Linear pair]

⇒ ∠PAT = 180° – ∠РАB

= 180° – 60°

= 120°

∠APT = ∠PBA = 30°   ...[Angles in alternate segments]

Now, ∠APT + ∠PАT + ∠PTA = 180°   ...[In ΔРАТ]

⇒ ∠PТА = 180° – (30° + 120°)

⇒ ∠PТА = 30°