Q. 24.5( 38 Votes )

If the angle betw

Answer :


Let AP and BP are two tangents from an external point P on a circle with center O, at points A and B respectively.


Angle with AP and BP,
APB = 60° [Given]


In ΔAOP and ΔBOP


AP = BP [Tangents drawn from an external point to a circle are equal]


OP = OP [Common]


OA = OB [Radii of same circle]


ΔAOP ΔBOP [By Side-Side-Side Criterion]


OPA = OPB [Corresponding parts of congruent triangles are equal]


Also,


OPA + OPB = APB


OPA + OPA = 60°


2OPA = 60°


OPA = 30°


Also, OA AP [Tangent drawn at a point on the circle is perpendicular to the radius through point of contact]


In ΔOAP,



[As OA = radius of circle = a]

 



OP = 2a

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