Question

Tangent AP and AQ are drawn to circle with centre 'Ofrom an external point A. Prove that angle PAQ= 2 angle OPQ​

Answer 1

Answer:

Step-by-step explanation:

OP=OQ (Radius of same circle)

Thus, ∠OPQ=∠OQP (Angle opposite to equal sides are equal)

In △OPQ, the sum of the angles is 180 ° that is

∠OPQ+∠OQP+∠POQ=180°

But ∠OPQ=∠OQP, therefore,

∠OPQ+∠OQP+∠POQ=180 °

∠OPQ+∠OPQ+∠POQ=180°

2∠OPQ+∠POQ=180 °

2∠OPQ=180° −∠POQ........(1)

We also know that

∠POQ+∠PAQ=180 °

∠PAQ=180°−∠POQ........(2)

From equations 1 and 2, we get

2∠OPQ=∠PAQ

Hence, ∠PAQ=2∠OPQ.