Question

prove that lengths of tangent drawn from an external point to a circle are equal

Answer 1

Dear friend..hi 

Given: PT and TQ are two tangent drawn from an external point T to the circle C (O, r).
To prove: PT = TQ
Construction: Join OT.
Proof: We know that, a tangent to circle is perpendicular to the radius through the point of contact.
∴ ∠OPT = ∠OQT = 90°
In ΔOPT and ΔOQT,
OT = OT  (Common)
OP = OQ  ( Radius of the circle)
∠OPT = ∠OQT  (90°)
∴ ΔOPT ΔOQT  (RHS congruence criterion)
⇒ PT = TQ  (CPCT)
Thus, the lengths of the tangents drawn from an external point to a circle are equal.
Cheers!

Answer 2

Answer:

Check your answer please