MathNet 2011 Question 67

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 $\ell$ and $CD$ are $H$ and $K$, respectively. Prove that the lines $EF$ and $HK$ are perpendicular.
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