Question

In the given figure, PQ is a tangent to the circle with centre O. If ∠OPQ = x, ∠POQ = y, then x + y is ______.

Options

• 45°

• 90°

• 60°

• 180°

Answer 1

In the given figure, PQ is a tangent to the circle with centre O. If ∠OPQ = x, ∠POQ = y, then x + y is 90°.

Explanation:

Given, ∠OPQ = x, ∠POQ = y

∠OQP = 90°       ...(∵ Radius is perpendicular to the tangent at the point of contact.)

In ΔOPQ,

∠OPQ + ∠POQ + ∠OQP = 180°      ...(angle sum property)

`\implies` x + y + 90° = 180°

`\implies` x + y = 180° – 90° = 90°