Q28 of 34 Page 1

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


Required to prove -: ∠PTQ = 2∠OPQ


Let ∠PTQ = θ


Now by the theorem TP = TQ. So, TPQ is an isosceles triangle


∠TPQ = ∠TQP = 1/2 (180° – θ)


= 90° - 1/2 θ


∠OPT = 90°


∠OPQ = ∠OPT – ∠TPQ = 90° – (90° – 1/2 θ)


= 1/2 θ


= 1/2 ∠PTQ


∠PTQ = 2∠OPQ


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