Question

Find the radius of the circle inscribed in the triangle.

Short answer

The radius of the circle is, $2\sqrt{2}$.

Step-by-step solution

Step 1. Given information.

The given figure is,

Step 2. Concept used.

In any triangle,

$s=\frac{a+b+c}{2}$where a and b are c the sides of the triangle.

Here,

$\begin{array}{l}a=12\\ b=12\\ c=8\end{array}$

Step 3. Put the values to find s.

$\begin{array}{c}s=\frac{12+12+8}{2}\\ s=\frac{32}{2}\\ s=16\end{array}$

Let the radius of circle be$r.$

Step 4. Formula used.

The radius of the circle inscribed in the triangle is given by the formula,

$\begin{array}{c}{r}^2=\frac{\left(s-a\right)\left(s-b\right)\left(s-c\right)}{s}\\ r^2=\frac{\left(16-12\right)\left(16-12\right)\left(16-8\right)}{16}\\ r^2=\frac{4\times 4\times 8}{16}\\ r=\sqrt{8}\\ r=2\sqrt{2}\end{array}$

Step 5. Neglect negative sign. 

Since, length is positive,

So, neglecting the negative value.

Therefore, the radius of the circle is, $2\sqrt{2}$.