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Question

As shown in the given figure two chord AB and CD of the same circle are parallel to each other. P is the centre of the circle
Show that CPA=DPB


Solution


In PCD, PC=PDi.e., PCD is an isosceles triangle.Hence, 1=2   [Angles oppsite to equal sides (PCand PD) are equal]2=3   (Correcponding angles)1=4   (Correcponding angles) 3=4    ...(i)   Similarly, in APB, we have:AP=BPi.e., APB is an isosceles triangle.Hence, 7=8   [Angles oppsite to equal sides (AP and BP) are equal]   .....(ii)5=180°-36=180°-4 5=6      (from(i))   ....(iii)

Now, 5+7+9=6+8+10   (Angle sum property)6+8+9=6+8+10   (from(ii) and (iii))9=10

CPA=DPB

Mathematics
Mathematics (Geometry)
Standard X

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