A triangle with sides 13 cm, 14 cm and 15 cm is inscribed in a circle. The radius of the circle is :

Answer: Option D

$$\begin{array}{rl}& s=\frac{13+14+15}{2}=\frac{42}{2}=21\\ & \therefore △=\sqrt{21\times 8\times 7\times 6}\\ & =\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)}\\ & =\left(2\times 2\times 3\times 7\right)\\ & =84c{m}^2\end{array}$$
Radius of circle :
$$\begin{array}{rl}& =\left(\frac{13\times 14\times 15}{4\times 84}\right)c{m}^2\\ & =\left(\frac{65}{8}\right)cm\\ & =8.125cm\end{array}$$