Problem 16. Given a parallelogram $A B C D$. Point $M$ is the midpoint of segment $A B$. Point $K$ lies on segment $A D$ and $A K: K D=1: 2$. Find in what ratio point $P$, the intersection of segments $A C$ and $M K$, divides segment $M K$.
Solution. Consider this parallelogram as the image of a square $ABCD$ with a side length of 6. The segment $AP$ is the angle bisector of the right angle of triangle $KAM$. Therefore, $KP: PM = AK: AM = \frac{1}{3} AD: 0.5 \quad AB = 2: 3$.