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Tangents at the two ends of a chord meet at an external point C. If the chord subtends 100° at the centre, the angle ACB between the two tangents equals:
Answer & Solution
Correct answer: B.
1. The angle between the radii to the chord ends equals the central angle of the chord, namely 100°.
2. The angle between two tangents drawn from an external point and the corresponding central angle are supplementary.
3. So the tangent-tangent angle equals 180° − 100° = 80°.
4. Equivalently, the quadrilateral OACB has opposite angles at A and B both right, so the remaining pair sums to 180°.
5. Thus angle ACB = 80°.
_Source: SCERT Kerala Std X Mathematics Part-2, Chapter 7 "Tangents" (pp 159-172, 2019 ed.)._
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