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प्रश्न
Prove that the length of tangents drawn from an external point to a circle are equal.
सिद्धांत
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उत्तर
Given: AP and BP are tangents of circle having centre O.
To Prove: AP = BP
Construction: Join OP, AO and BO
Proof: ∠OAP and ∠OBP
OA = OB ...[Radius of circle]
OP = OP ...[Common side]
OAP = OBP = 90° ...(Radius – tangent angle)
ΔOAP ≅ ΔOBP ...[RHS congruency rule]
AP = BP ...[CPCT]
Hence Proved.
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