1.

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

Answer»

Required to prove -: ∠PTQ = 2∠OPQ 

Let ∠PTQ = θ 

Now by the theorem TP = TQ. 

So, TPQ is an isosceles triangle 

∠TPQ = ∠TQP = \(\frac{1}{2}\) (180° - θ) = 90° - \(\frac{1}{2}\) θ 

∠OPT = 90° 

∠OPQ = ∠OPT - ∠TPQ = 90° - (90° - \(\frac{1}{2}\)θ) = \(\frac{1}{2}\)θ 

= \(\frac{1}{2}\) ∠PTQ 

∠PTQ = 2∠OPQ



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