Question

What is the radius of the circle circumscribed in a triangle with the sides 5cm,12cm and 13cm?

Answer 1

Let $AB=5cm$ $BC=12cm$ and $CA=13cm$

In $\Delta ABC$

${AB}^2+{BC}^2=25+144=169$

${CA}^2={13}^2=169$

${AB}^2+{BC}^2={CA}^2=169$

$\Delta ABC$ is right angled triangle at $B$ hypotenuse $AC$.

We know that midpoint hypotenuse is equidistant from $BD$ and $C$

Radius $=\frac{13}{2}=6.5cm$