Question

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

Answer 1

Answer:

MATHS

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

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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)