Question

In the given figure, O is centre of the circle and PQ is a tangent. If angle OAB = x; the measure of angle ABP, in terms of x, is:

Options

• x

• 180° − 2x

• 90° + x

• 90° − x

Answer 1

90° − x

Explanation:

From figure,

In △OAB,

OA = OB (Radius of same circle)

We know that,

Angles opposite to equal sides are equal.

⇒ ∠OBA = ∠OAB = x

We know that,

Tangent at any point of a circle and the radius through this point are perpendicular to each other.

∴ OB ⊥ PQ

∴ ∠PBO = 90°

From figure,

∠ABP = ∠PBO − ∠OBA = 90° - x.