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प्रश्न
If two tangents are drawn to a circle from an external point, show that they subtend equal angles at the centre.
बेरीज
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उत्तर
Given: A circle with centre O and a point A outside it. Also, AP and AQ are the two tangents to the circle
To prove: ∠AOP = ∠AOQ
Proof: In ΔAOP and ΔAOQ, we have
AP = AQ ...[Tangents from an external point are equal]
OP = OQ ...[Radii of the same circle]
OA = OA ...[Common side]
∴ ΔAOP ≅ ΔAOQ ...[By SSS - congruence]
Hence, ∠AOP = ∠AOQ (c.p.c.t).
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