Question

In the given figure, O is the centre of the circle. AB is the tangent to the circle at the point P. If ∠PAO = 30° then ∠CPB + ∠ACP is equal to ______.

Options

• 60°

• 90°

• 120°

• 150°

Answer 1

In the given figure, O is the centre of the circle. AB is the tangent to the circle at the point P. If ∠PAO = 30° then ∠CPB + ∠ACP is equal to 90°.

Explanation:

∠DPC = 90°   ...[Angle in a semicircle]

And ∠DPA = ∠DCP   ...[Angles in alternate segments]

Now, ∠CPB + ∠DPA + ∠DPC = 180°

⇒ ∠CPB + ∠DPA = 90°

⇒ ∠CPB + ∠DCP = 90°

⇒ ∠CPB + ∠ACP = 90°