Question 71
Let $ABC$ be a non-right triangle with $M$ the midpoint of $BC$. Let $D$ be a point on the line $AB$ such that $CA = CD$ and let $E$ be a point on the line $BC$ such that $EB = ED$. The parallel to $ED$ through $A$ meets the line $MD$ at the point $I$ and the line $AM$ meets the line $ED$ at the point $J$. Show that the points $C$, $I$ and $J$ are collinear.