Q. 75.0( 1 Vote )

# 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°

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