Q. 3 B3.7( 3 Votes )

The picture shows

Answer :

Construction: Label the diagram.



In ΔAOP and ΔBOP


OA = OB [Radii of same circle]


OP = OP [Common]


OAB = OBP = 90° [Tangent at any point is perpendicular to the radius through point of contact]


ΔAOP ΔBOP [By Right Angle - Hypotenuse - Side Criteria]


⇒ ∠AOP = BOP [Corresponding parts of congruent triangle are equal]


OP bisects AOB.


i.e. the line joining the centre and the points where the tangents meet bisects the angle between the radii.


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