Question
Prove that the length of tangents drawn from an external point to a circle is equal.
Solution
Given: TP and TQ are two tangent drawn from an external point T to the circle C (O, r).
To prove: TP = TQ
Construction: Join OT
Proof: we know that a tangent to the circle is perpendicular to the radius through the point of contanct.
∴ ∠OPT = ∠OQT = 90o
In Δ OPT and ΔOQT
OT = OT (common)
OP = OQ (radius of the circle)
∠OPT = ∠OQT (90o)
∴ ∠OPT = ∠OQT (RHS congruence criterion)
⇒ TP = TQ (CPCT)
Hence, the length of the tangents drawn from an external point to a circle is equal.
