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}