Question

Two tangents TP and TQ are drawn from an external point T to a circle with centre O as shown in figure. If they are inclined to each other at an angle of 100°, then what is the value of ∠POQ?

Answer 1

Use the tangent theorem: angle PTQ = 2·angle OPQ.

Given PTQ = 100°, so OPQ = `100^circ/2` = 50°.

In isosceles triangle OPQ (OP = OQ), the base angles are each `(180^circ - ∠POQ)/2` and OPQ is one of these base angles.

Thus `(180^circ - ∠POQ)/2 = 50^circ` 

⇒ 180° – ∠POQ = 100°

⇒ ∠POQ = 80°