Answer :

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 90^{o})

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

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

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