Q. 264.0( 4 Votes )

In the given figure, O is the center of the circle. AB is the tangent to the circle at the point P. If PAO = 30° then CPB + ACP is equal to


A. 60°

B. 90°

C. 120°

D. 150°

Answer :


In given Figure, Join OP


In OPC,


OP = OC [Radii of same circle]


OCP = OPC


[Angles opposite to equal sides are equal]


ACP = OPC


[As OCP = ACP] …[1]


Now,


OPB = 90°


[Tangents drawn at a point on circle is perpendicular to the radius through point of contact]


OPC + CPB = 90°


ACP + CPB = 90° [By 1]


So,


CPB + ACP = 90°

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