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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


Your Answer
A
43
Your Answer
B
1273
Correct Answer
C
12+73
Your Answer
D
None of the above

Solution

The correct option is D 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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