18. (GDR 4) Given an isosceles triangle $A B C$ with a right angle at $C$, construct the center $M$ and radius $r$ of a circle cutting on segments $A B, B C, C A$ the segments $D E, F G$, and $H K$, respectively, such that $\angle D M E+\angle F M G+\angle H M K=180^{\circ}$ and $D E: F G: H K=A B: B C:$ $C A$
18. Let $U$ be the midpoint of the segment $A B$. The point $M$ belongs to $C U$ and $C M=(\sqrt{5}-1) C U / 2, r=C U \sqrt{\sqrt{5}-2}$.