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