Home > Geometry, IMO, Olympiad > Balkan Mathematical Olympiad 2011 Problem 1

## Balkan Mathematical Olympiad 2011 Problem 1

Let $ABCD$ be a cyclic quadrilateral which is not a trapezoid and whose diagonals meet at $E$. The midpoints of $AB$ and $CD$ are $F$ and $G$ respectively, and $\ell$ is the line through $G$ parallel to $AB$. The feet of the perpendiculars from $E$ onto the lines $\ell$ and $CD$ are $H$ and $K$, respectively. Prove that the lines $EF$ and $HK$ are perpendicular.

BMO 2011 Problem 1