Question

In the given figure, PA is a tangent to the circle drawn from the external point P and PBC is the secant to the circle with BC as diameter. If ∠AOC = 130°, then find the measure of ∠APB, where O is the centre of the circle.

Answer 1

In ΔAPO, ∠AOC is the exterior angle

∴ From exterior angle property.

∠AOC = ∠PAO + ∠APB  ...`{{:(∵ ∠AOC = 130^circ ("Given")),(∠PAO = 90^circ "(radius and tangent"),("are" ⊥ "to each other at the point of contact)"):}`

`\implies` 130° = 90° + ∠APB

`\implies` ∠APB = 130° – 90°

`\implies` ∠APB = 40°