Question

In the given figure, PA is a tangent from an external point P to a circle with centre O and diameter AB. If ∠POB = 115°, then the measure of ∠APO is:

Options

• 25°

• 30°

• 20°

• 65°

Answer 1

25°

Explanation:

Given, PA is a tangent.

OP ⟂ PA (radius ⟂ tangent)

∠POB = 115°

AB is a diameter.

A, O, B are in a straight line.

So ∠AOB = 180°

∠AOP = ∠AOB − ∠POB

= 180° − 115°

= 65°

Now in ΔAOP:

OP ⟂ PA ⇒ ∠OPA = 90°

We need ∠APO (the angle at P):

∠APO = 90° − ∠AOP

= 90° − 65°

= 25°