Q15 of 22 Page 126

Two circles with centres A and B interest each other at the points C and D. The centre lies on the circle with centre A. If ∠CQD = 70°, let us find the value of ∠CPD.

In circle with centre B, by the theorem:-


The angle formed at the centre of a circle by an arc, is double of the angle formed by the same arc at any point on circle.


∠CBD = 2 ∠CQD = 140°


Now, since B lies on the circle with centre A, therefore, quadrilateral CPDB is cyclic quadrilateral.


We also know that, the sum of opposite sides in a cyclic quadrilateral is equal to 180°


⇒ ∠CPD + ∠CBD = 180°


On substituting the value in above equation, we get,


⇒ ∠CPD = 180 – 140


⇒ ∠CPD = 40°


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