Book: RS Aggarwal - Mathematics
Chapter: 12. Circles
Subject: Maths - Class 10th
Q. No. 26 of Multiple Choice Questions (MCQ)
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26
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
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°
