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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.
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°