Question 73
Given a triangle $ABC$, let $D$ be the midpoint of the side $AC$ and let $M$ be the point that divides the segment $BD$ in the ratio $1/2$; that is, $MB/MD = 1/2$. The rays $AM$ and $CM$ meet the sides $BC$ and $AB$ at points $E$ and $F$, respectively. Assume the two rays are perpendicular: $AM \perp CM$. Show that the quadrangle $AFED$ is cyclic if and only if the line of support of the median from $A$ in triangle $ABC$ meets the line $EF$ at a point situated on the circle $ABC$.
BMO Shortlist 2011, Saudi Arabia
BMO Shortlist 2011, Saudi Arabia