Q29 of 47 Page 1

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


Given: PT and PS are tangents from an external point P to the circle with center O.


To prove:


PT = PS


Construction: Join O to P, T, and S


Proof:


In ΔOTP and ΔOSP,


OT=OS …[radii of same circle


OP=OP …[Common


∠OTP=∠OSP …[Each 90o


∴ ΔOTP≅ΔOSP …[R.H.S.


Hence, PT =PS …[c.p.c.t.


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