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Question

In radius of a circle which is inscribed in a isosceles triangle one of whose angle is 2π3 is 3, then area of triangle (in sq units) is

A
43
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B
1273
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C
12+73
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D
None of the above
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Solution

The correct option is C 12+73
Let AB=AC=a and A=120
Area of triangle =12a2sin120
Where a=AD+BD=3tan30+3cot15=1+3tan(4515)



a=1+3(1+tan45tan30ta45tan30)
=1+3(3+131)=4+23
Area of triangle
=12(4+23)2(32)=(12+73) sq units

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