Q. 144.3( 6 Votes )

# In the given figure, PA and PB are two tangents to the circle with center O. If ∠APB = 60° then find the measure of ∠OAB.

Answer :

In the given figure, PA and PB are two tangents from common point P

PA = PB

[ Tangents drawn from an external point are equal]

PBA = PAB

[ Angles opposite to equal angles are equal] …[1]

By angle sum property of triangle in APB

APB + PBA + PAB = 180°

60° + PAB + PAB = 180° [From 1]

2PAB = 120°

PAB = 60° …[2]

Now,

OAP = 90° [Tangents drawn at a point on circle is perpendicular to the radius through point of contact]

OAB + PAB = 90°

OAB + 60° = 90° [From 2]

OAB = 30°

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