Q24 of 46 Page 1

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


Given : A circle with center O , two tangents PT and PQ are drawn from an external point P


to the points T and Q on circle.


To prove : PT = PQ


Construction : Join OP


Proof :


In △POT and △POQ


OT = OQ [radii of same circle]


∠PTO = ∠PQO = 90° [tangent drawn at a point on a circle is perpendicular to the radius through point of contact]


OP = OP [common]


△POT ≅ △POQ [By RHS criterion]


PT = PQ [By CPCT]


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