11.15. From a point $M$, lying on the side $A B$ of an acute-angled triangle $A B C$, perpendiculars $M P$ and $M Q$ are dropped to the sides $B C$ and $A C$. For what position of point $M$ is the length of the segment $P Q$ minimal?
11.15. Points $P$ and $Q$ lie on the circle constructed on segment $C M$ as its diameter. In this circle, the constant angle $C$ subtends the chord $P Q$, so the length of the chord $P Q$ will be minimal if the diameter $C M$ of the circle is minimal, i.e., $C M$ is the altitude of triangle $A B C$.