Q. 54.2( 17 Votes )

In the given figu

Answer :

Given: PA and PB are tangents to a circle with center O


To show : A, O, B and P are concyclic i.e. they lie on a circle i.e. AOBP is a cyclic quadrilateral.


Proof:


OB PB and OA AP


[Tangent at any point on the circle is perpendicular to the radius through point of contact]


OBP = OAP = 90°


OBP + OAP = 90 + 90 = 180°


AOBP is a cyclic quadrilateral i.e. A, O, B and P are concyclic.


[ As we know if the sum of opposite angles in a quadrilateral is 180° then quadrilateral is cyclic]


Hence Proved.


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