3. Let $\triangle A B C$ be a right triangle with a right angle at vertex $C$. $M$ is a point on side $A B$ and $K$ and $L$ are the feet of the perpendiculars dropped from $M$ to sides $A C$ and $B C$, respectively. Which point should $M$ be for the distance $\overline{K L}$ to be the smallest.

![](https://cdn.mathpix.com/cropped/2024_06_05_162556eb92784f75b3beg-3.jpg?height=358&width=656&top_left_y=1640&top_left_x=246)
Solution. Let's note that MLCK is a rectangle. Then its diagonals are equal. So $\overline{C M}=\overline{K L}$. The segment $C M$ is the smallest when it is the height of triangle $\triangle A B C$. Therefore, $M$ must be the foot of the perpendicular dropped from $C$.