**Q)** Two tangents TP and TQ are drawn to a circle with centre 0 from an external point T. Prove that ∠PTQ = 2∠OPQ.

**Ans:**

TP = TQ

⇒ ∠TPQ = ∠TQP

Let ∠PTQ be θ

⇒ ∠TPQ = ∠TQP =

= 90° – ^{ }

Now, ∠OPT = 90°

⇒ ∠OPQ = 90°^{ } – [90° – ] =

^{ ∠PTQ = 2 ∠OPQ …. Hence Proved}