G-4 Cyclic Equilateral

Obtain first the radius of the from the given area of the circle. This gives the value of the radius,

r = $\sqrt{\frac{150Π}{Π}}$ = 5 $\sqrt{6}$ units.

Since the triangle is inscribed in a circle, then r= $\frac{s}{\sqrt{3}}$

5 $\sqrt{6}$ = $\frac{s}{\sqrt{3}}$ or s = 15 $\sqrt{2}$ units,

Hence the area of the triangle is,

A = $\frac{(15\sqrt{2})^{2}}{4}$ = $\frac{225\sqrt{3}}{2}$ = $\frac{a\sqrt{b}}{c}$

The sum of a+b+c = 225+ 3 + 2 = $\boxed{230}$