An isosceles ΔMNP is inscribed in a circle. If MN = MP = 16√5 cm, and NP = 32 cm, what is the radius (in cm) of the circle?

Solution (By Examveda Team)

$$\eqalign{ & {\text{Height of }}\Delta {\text{MND}} \cr & = \sqrt {{{\left( {16\sqrt 5 } \right)}^2} - {{\left( {\frac{{32}}{2}} \right)}^2}} \cr & = \sqrt {{{\left( {16\sqrt 5 } \right)}^2} - {{\left( {16} \right)}^2}} \cr & = 16\sqrt {5 - 1} \cr & = 16 \times 2 \cr & = 32 \cr & {\text{R}} = \frac{{{\text{abc}}}}{{4\Delta }} = \frac{{16\sqrt 5 \times 16\sqrt 5 \times 32}}{{4 \times \frac{1}{2} \times 32 \times 32}} = 20 \cr} $$