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
B
1273
C
12+73
D
None of the above

Solution

## The correct option is D 12+7√3Let AB=AC=a and ∠A=120∘ ∴   Area of triangle =12a2sin120∘ Where a=AD+BD=√3tan30∘+√3cot15∘=1+√3tan(45∘−15∘) ⇒a=1+√3(1+tan45∘tan30∘ta45∘−tan30∘) =1+√3(√3+1√3−1)=4+2√3 ∴ Area of triangle =12(4+2√3)2(√32)=(12+7√3) sq units

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