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  • Prove that the lengths of tangents drawn from an external point to a circle are equal.   

Prove that the lengths of tangents drawn from an external point to a circle are equal. 

 

Answers (1)

Let AP and AQ two tangents draw from external point A to a circle C (o,r)

To prove AP = AQ 

construction join OA , OP and OQ 

In 

\Delta OPA \: \: and \: \: \Delta OQA

we know that the tangent at any point on a circle is perpendicular to radius through point of contact 

so, OP \perp AP \: \: and \: \: OQ \perp AQ \\\\ \angle OPA = \angle OQA = 90 \degree ---- (1 ) \\\\ OP = OQ \\\\ OA = OA \\\\

BY RHS - criterion of congruence, we get 

\Delta OPA \cong \Delta OQA \\\\ AP= AQ

Posted by

Safeer PP

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