Q24 of 49 Page 1

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


Given: PT and TQ are two tangents from an external point T to a circle


To prove: PT = TQ


In ΔPTO and ΔQTO,


OP = OQ [Radius of the same circle]


∠OPT = ∠OQT = 90° [Tangent to a circle is perpendicular to the radius at the point of contact]


OT = OT [Common]


⸫ ΔPTO ≅ ΔQTO [S.A.S]


⸫ PT = TQ [C.P.C.T.C]


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