Multiple choice

A,B and C are three points on a circle.The tangent at C meets BA produced at T. Given ∠ ATC = 360 and ∠ ACT = 480, the angle subtended by AB at the centre of the circle is - A,B तथा C एक वृत्त पर तीन बिंदु है। उसमें C पर खींची स्पर्श रेखा BA को बढ़ाकर T पर मिल जाती है। तद्नुसार, यदि ∠ ATC = 360 तथा ∠ACT = 480 दिया हो,तो AB द्वारा वृत्त के केंद्र पर बनाया कोण कितना हो जाएगा?

  1. 48o

  2. 36o

  3. 96o

  4. 120o
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C Correct answer
Explanation

By the alternate segment theorem, ∠ABC = ∠ACT = 48°. In triangle ABC, ∠BAC = 180° - ∠ATC - ∠ACT = 180° - 36° - 48° = 96°. The angle subtended by chord AB at the center is twice the angle subtended at any point on the circumference, so central angle = 2 × ∠ACB. ∠ACB = 180° - 96° - 48° = 36°. Central angle = 2 × 48° = 96°.

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