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Question

PA and PB are the two tangents drawn to the circle. O is the center of the circle. A and B are the points of contact of the tangents PA and PB with the circle. If OPA=35, then find POB.

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Solution


Given, PA and PB are two tangents.And OPA=35o.

We know that line joining point of contact of tangent to centre of circle is perpendicular to tangent.
OAP=OBP=90...(i)

In, OAP, by angle sum property of a triangle,
OAP+APO+POA=180o
AOP=1803590
AOP=55

Consider OAP and OBP,
OA=OB (radius )
OAP=OBP=90 (from (i))
PA=PB (Tangents from an external point to the circle are equal in length.)

OAPOBP (By SAS congruence criterion)

By CPCT,AOP=BOP.
Thus, BOP=55.


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