Q22 of 47 Page 1

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

It is given in the question that, PT and PS are the tangents from an external point to the circle with center O


We have to prove that, PT = PS


Construction: Join O to P, T and S


Proof: Firstly, in triangle OTP and OSP we have:


OT = OS (Radii of circle are equal)


OP = OP (Common)


∠ OTP = ∠ OSP (Each angle is equal to 90o)


∴ ∠ OTP = ∠ OSP (By R.H.S congruence rule)


Hence, PT = PS (By c.p.c.t)


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