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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 = ?
Options
60°
30°
15°
45°
MCQ
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Solution
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°
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