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.


Answer :

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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