Question 41
In triangle $ABC$, $\angle BCA=90^\circ$, and $D$ is the foot of the altitude from $C$. Take $X$ in the interior of segment $CD$. Point $K$ lies on segment $AX$ and satisfies $BK=BC$. Similarly, $L$ lies on segment $BX$ and satisfies $AL=AC$. If $M$ is the intersection of segments $AL$ and $BK$, prove that $MK=ML$.