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Question

If an isosceles ABC in which AB=AC=6 cm is inscribed in a circle of radius 9cm. Find area of the triangle.
1061929_2ed5df4d4b5549a3b315dfa68df00d54.png

A
8cm2
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B
82cm2
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C
6cm2
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D
none
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Solution

The correct option is C 82cm2
Let AP=xcm.
PO=(9x)cm
In APC
AP2=36PC2
AP=36PC2
Similarly, PC2=36=x2
In OPC
OC2=OP2+PC2
g2=(gx)2+36x2
g2=81+x218x+36x2
18x=36
x=2cm
PC=36x2=364
=32=42
BC=2×PC=82cm
a from centre of circle on any cheared bisects the chord.
Area=12×BC×AP
=12×82×2
=12×82×2=82cm2

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