The inradius of a circle inscribed in an isosceles triangle

MATHEMATICS · Single correct · A Level · Mathematics · Trigonometry · Trigonometry

Problem

The inradius of a circle inscribed in an isosceles triangle, one of whose angles is

\frac{2\pi}{3}

, is

\sqrt{3}

. Then the area of the triangle, in square units, is (1)

4\sqrt{3}

(2)

12-7\sqrt{3}

(3)

12+7\sqrt{3}

(4) None of the above