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Tangents at points A and B on a circle centred at O meet at an external point C. In the quadrilateral OACB, why is the quadrilateral cyclic?
Answer & Solution
Correct answer: A.
1. OA is a radius and CA is a tangent at A, so angle OAC = 90°.
2. Similarly OB is a radius and CB is a tangent at B, giving angle OBC = 90°.
3. The two opposite angles at A and B add to 90° + 90° = 180°.
4. A quadrilateral is cyclic if and only if a pair of opposite angles sum to 180°.
5. Hence OACB is cyclic by the opposite-angle criterion, not by side or diagonal properties.
_Source: SCERT Kerala Std X Mathematics Part-2, Chapter 7 "Tangents" (pp 159-172, 2019 ed.)._
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