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

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