Question 24
A triangle $ABC$ is given with the points $D$ on the side $AB$, $E$ on the side $BC$ and $F$ on the side $AC$, such that the line $CD$ is perpendicular to the side $AB$, the line $DE$ is perpendicular to the side $BC$ and the line $DF$ is perpendicular to the side $AC$. Prove that the points $A$, $B$, $E$ and $F$ lie on the same circle.