Multiple choice

The tangents at two points A and B on the circle with centre O intersect at P, if in quadrilateral PAOB, ∠AOB : ∠APB = 5 : 1. then measure of ∠APB is - O केन्द्र वाले वृत्त के दो बिन्दुओं पर स्पर्श रेखा बिन्दु P पर प्रतिच्छेदित करती है, यदि चतुर्भुज PAOB में, ∠AOB : ∠APB = 5:1 हो, तो ∠APB की माप है-

  1. 60o

  2. 45o

  3. 30o

  4. 90o
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C Correct answer
Explanation

Since PA and PB are tangents to the circle, OA ⟂ PA and OB ⟂ PB. In quadrilateral PAOB, ∠OAP = ∠OBP = 90°. Sum of angles = 360°, so ∠AOB + ∠APB + 90° + 90° = 360°, giving ∠AOB + ∠APB = 180°. Given the ratio 5:1, let ∠AOB = 5x and ∠APB = x. Then 6x = 180°, so x = 30°.

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