Question

In Fig. 3, two tangents PQ are PR are drawn to a circle with centre O from an external point P. Prove that ∠QPR = 2 ∠OQR.

Answer 1

Given a figure as shown. We have to prove that

Join OR

We know that sum of opposite angles of a cyclic quadrilateral

Therefore in quadrilateral PQOR,

…… (1)

In

[Since OQ, OR are radii of the circle]

Therefore is an isosceles triangle.

Hence [Angles opposite to equal side of isosceles triangle]

Now, [since,]

[From (1)]

Hence proved.