Whenever a Circle with radius \(r\) is inscribed inside an Equilateral triangle with each side \(a\), then \(r = \frac{a}{2\sqrt{3}}\)

Area of Circle \(= πr^2 = π(\frac{a}{2\sqrt{3}})^2 = \frac{πa^2}{12}\)

Area of an Equilateral triangle \(= \frac{\sqrt{3}a^2}{4}\)

Now, % area of the triangle that lies within the circle = (Area of Circle / Area of triangle) x 100

\(= (\frac{πa^2}{12})(\frac{4}{\sqrt{3}})(100)\)

\(= \frac{π}{3\sqrt{3}}(100) = 60.45\)%

Hence, option C