Question

What is the radius of the circumcircle of a triangle whose sides are $30cm,36cmand30cm?$

Answer 1

Find the radius of the circumcircle of a triangle.

The triangle's dimension are $30\mathrm{cm},36\mathrm{cm},30\mathrm{cm}.$

In $∆ABC$, By Pythagoras Theorem :

$\begin{array}{rcl}\mathrm{AB}& =& {\mathrm{AC}}^2+{\mathrm{BC}}^2\\ & \Rightarrow & \mathrm{AC}=\sqrt{{30}^2-{18}^2}\\ & \Rightarrow & \mathrm{AC}=24\end{array}$

Area of$∆ABC$:

$\begin{array}{rcl}\mathrm{Ar}(△\mathrm{ABC})& =& \frac{1}{2}\times \mathrm{base}\times \mathrm{height}\\ & =& \frac{1}{2}\times 24\times 36\\ & =& 432\end{array}$

The radius of the circle center is $\frac{\mathrm{abc}}{4\times \mathrm{Area}(△\mathrm{ABC})}$.

Hence put the respective value of sides and area to find the radius:

$\begin{array}{rcl}\mathrm{Radius}& =& \frac{\mathrm{abc}}{4\times \mathrm{Area}(△\mathrm{ABC})}\\ & =& \frac{30\times 30\times 36}{4\times 432}\\ & =& 18.75\mathrm{cm}\end{array}$

Hence, the radius of the circumcircle of a triangle is $18.75\mathrm{cm}$.