Problem

Source: 2nd European Mathematical Cup

Tags: geometry, circumcircle, geometry unsolved



Given a triangle $ABC$ let $D$, $E$, $F$ be orthogonal projections from $A$, $B$, $C$ to the opposite sides respectively. Let $X$, $Y$, $Z$ denote midpoints of $AD$, $BE$, $CF$ respectively. Prove that perpendiculars from $D$ to $YZ$, from $E$ to $XZ$ and from $F$ to $XY$ are concurrent.