Question

Prove that "The lengths of tangents drawn form an external point to a circle are equal"​

Answer 1

Answer:

Given : PT and TQ are two tangents drawn from an external point T to the circle C(o,r)

To prove : PT=TQ

Proof : We know that a tangent to the circle is ⊥ to the radius through the point of contact. So, ∠OPT=∠OQT,

OT=OT (common)

∠OPT=∠OQT=90  

∘

 (Tangent and radius are perpendicular at point of contact)

OP=OQ= radius

∴ΔOPT≅ΔOQT (RHS congruence)

∴PT=TQ (by c.p.c.t)

So, length of the tangents drawn from an external point to circle are equal.

Step-by-step explanation: