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Question

In an isosceles triangle ABC, in which AB=AC=6cm, is inscribed in a circle of radius 9cm. Find the area of the triangle.

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Solution

Let AP=x

So, OP=9x

In APC

AP2=36PC2

AP=36PC2

Similarly, PC2=36x2

Now, In OPC

OC2=OP2+PC2

92=(9x)2+36x2

81=81+x218x+36x2

18x=36

x=2cm

PC=364=32=42

BC=82

Therefore, Area=12×b×h

Area=12×82×2=82cm2

989867_1083622_ans_11f32115b6d94bc388ec2df10935ccfb.jpg

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