Frankin 5.

In triangle $ABC$, the altitude and median drawn from vertex $A$ form (together with line $BC$) a triangle in which the bisector of angle $A$ is a median, and the altitude and median drawn from vertex $B$ form (together with line $AC$) a triangle in which the bisector of angle $B$ is a bisector. Find the ratio of the sides of triangle $ABC$.
Since the bisector of angle $B$ divides the angle between the height and the median in half, angle $B$ is a right angle. Therefore, the height drawn from vertex $A$ coincides with side $A B$, which means the bisector of angle $A$ divides side $B C$ in the

ratio of $1: 3$. Consequently, the ratio $A B: A C$ is also $1: 3$.

## Answer

$1: 2 \sqrt{2}: 3$