Problem

Let one angle of a triangle be

60^\circ

, the area of triangle is

10\sqrt{3}

and perimeter is 20 cm. If

a > b > c

where

a, b

and

c

denote lengths of sides opposite to vertices

A, B

and

C

respectively, then which of the following is(are) correct? a. Inradius of triangle is

\sqrt{3}

b. Length of longest side of triangle is 7 c. Circum-radius of triangle is

\frac{7}{\sqrt{3}}

d. Radius of largest escribed circle is

\frac{1}{12}