Multiple choice

Two tangents are drawn from a point P to a circle at A and B .O is the centre of the circle .If ∠AOP = 600 ,then ∠APB is -

  1. 600

  2. 300

  3. 1200

  4. 900
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A Correct answer
Explanation

Tangents from external point P are equal, so PA = PB. Triangle OAP is right-angled at A (radius perpendicular to tangent). In triangle OAP: angle OAP = 90°, angle AOP = 60°, so angle APO = 30°. Triangle APB is isosceles with PA = PB, so angle APB = 2 × angle APO = 60°. Assuming '600' means 60°.

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