# Inspired by Nihar Mahajan

Geometry Level 5

Let $$\color{brown}{\Delta ABC}$$ be a triangle with side $$\color{red}{AB = 12,} ~\color{blue}{BC=4\sqrt{5}}~ \& ~ \color{orange}{AC = 8\sqrt{2}}$$.

Also let $$\color{grey}{P,~Q~\& ~R}$$ be the points on side $$\color{indigo}{AB,~BC~ \& ~ CA}$$ respectively such that perimeter of $$\color{green}{\Delta PQR}$$ is minimum.

Find the inradius of $$\color{green}{\Delta PQR}$$.

Note: The picture is not drawn up to scale.

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