CBSE Class 10 Maths (Basic) 2020 · Paper 430/4/1 · Question 28(b)

Circles 3 marks Medium

In Figure-6, two tangents TP and TQ are drawn to a circle with centre O from an external point T. Prove that

∠ P T Q = 2 ∠ O P Q

Two tangents TP and TQ from external point T to a circle centred at O, with chord PQ (Figure-6)

Answer

Taking

∠ P T Q = x

, the isosceles triangle gives

∠ T P Q = 9 0^{\circ} - \frac{x}{2}

, and

∠ O P T = 9 0^{\circ}

yields

∠ O P Q = \frac{x}{2}

. Hence

∠ P T Q = 2 ∠ O P Q

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