PA and PB are two tangents drawn from an external point P to a circle with centre O. If ∠PBA = 65°, then ∠APB = _______.

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Solution

PA and PB are two tangents drawn from an external point P to a circle with centre O.

∴ PA = PB (Lengths of tangents drawn from an external point to a circle are equal)

In ∆APB,

PB = PA (Proved)

⇒ ∠PAB = ∠PBA (In a triangle, equal sides have equal angles opposite to them)

⇒ ∠PAB = 65° (∠PBA = 65°)

Also,

∠PAB + ∠PBA + ∠APB = 180° (Angle sum property of triangle)

⇒ 65° + 65° + ∠APB = 180°

⇒ ∠APB = 180° − 130° = 50°

PA and PB are two tangents drawn from an external point P to a circle with centre O. If ∠PBA = 65°, then ∠APB = _50°_.

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