In a triangle $ABC$ with $\angle BAC = 90^{\circ}$ let $BL$ be the bisector, $L\in AC$. Let $D$ be a point symmetrical to $A$ with respect to $BL$. Let $M$ be the circumcenter of $ADC$. Prove that $CM$, $DL$, and $AB$ are concurrent.
Source: IV Caucasus Mathematic Olympiad
Tags: geometry
In a triangle $ABC$ with $\angle BAC = 90^{\circ}$ let $BL$ be the bisector, $L\in AC$. Let $D$ be a point symmetrical to $A$ with respect to $BL$. Let $M$ be the circumcenter of $ADC$. Prove that $CM$, $DL$, and $AB$ are concurrent.