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JEE Advanced2006MathematicsProperties of TrianglesActual

Inradius of a circle which is inscribed in an isosceles triangle one of whose angle is 2 / 3 , is 3 , then area of triangle is

Options

  1. A4 3
  2. B12-7 3
  3. C12+7 3
  4. DNone of these

Correct answer

C. 12+7 3

Step-by-step solution

Let A B=A C and A=120^ Area of = 1 2 a^2 120^ where, a=A D+B D= 3 30^ + 3 15^ =1+ 3 ( 1+ 45^ 30^ 45^ - 30^ )=1+ 3 ( 3 +1 3 -1 ) a=4+2 3 Area of = 1 2 (4+2 3 )^2 ( 3 2 )=12+7 3

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