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 toA. 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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