Be $ABC$ a right triangle in $C$, with $BC=a$ and $AC=b$. In $BC$ is chosen a point $P$ and in $AC$ a point $Q$. Be $K$ and $H$ the perpendicular projections of $P$ and $Q$ respectively over the hypotenuse $AB$
Find the minimum value of the sum $KP+PQ+QH$ with respect to variables $a$ and $b$.
I made a drawing of how the problem should look like:
But to be honest, i don't see a way to start this problem. Any hints?
Hint: Reflect $A$ and $K$ along $\overline{BC}$ to $A'$ and $K'$, reflect $B$ and $H$ along $\overline{AC}$ to $B'$ and $H'$: