In the given figure, PA and PB are two tangents from an external point P to a circle with center O. If ∠PBA = 65°, find ∠OAB and ∠APB.

Question

In the given figure, PA and PB are two tangents from an external point P to a circle with center O. If ∠ PBA = 65°, find ∠ OAB and ∠ APB.

Philoid · Accepted Answer

In the given Figure,

PA = PB

[Tangents drawn from an external points are equal]

∠PBA = ∠PAB

[Angles opposite to equal sides are equal]

∠PBA = ∠PAB = 65°

In △APB

∠PAB + ∠PBA + ∠APB = 180°

65° + 65° + ∠APB = 180°

∠APB = 50°

Also,

OB ⏊ AP

[Tangents drawn at a point on circle is perpendicular to the radius through point of contact]

∠OAP = 90°

∠OAB + ∠PAB = 90°

∠OAB + 65° = 90°

∠OAB = 25°