Question 64
In a circle, consider two chords $[AB]$, $[CD]$ that intersect at $E$. The lines $AC$ and $BD$ meet at $F$. Let $G$ be the projection of $E$ onto $AC$. We denote by $M, N, K$ the midpoints of the segment lines $[EF]$, $[EA]$, and $[AD]$, respectively. Prove that the points $M, N, K, G$ are concyclic.
Marius Bocanu
Marius Bocanu