Question 102
A triangle $ABC$ is given in which $BC$ is the shortest side. Denote $M$ its midpoint. On the sides $AB$ and $AC$ take the points $X$ and $Y$, respectively, in such a way that $|BX| = |BC| = |CY|$. Denote $Z$ the intersection point of lines $CX$ and $BY$. Prove that the line $ZM$ passes through the centre of the excircle escribed to the side $BC$ of the triangle.