Q. 24.4( 7 Votes )

In the given figure, PA and PB are two tangents to the circle with center O. If APB = 50° then what is 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°


50° + PAB + PAB = 180° [From 1]


2PAB = 130°


PAB = 65° [2]


Now,


OAP = 90°


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


OAB + PAB = 90°


OAB + 65° = 90° [From 2]


OAB = 25°


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