Question 23
Five distinct points $A, B, C, D$ and $E$ lie on a line with
$$
|A B|=|B C|=|C D|=|D E|.
$$
The point $F$ lies outside the line. Let $G$ be the circumcentre of triangle $A D F$ and $H$ be the circumcentre of triangle $B E F$. Show that lines $G H$ and $F C$ are perpendicular.
$$
|A B|=|B C|=|C D|=|D E|.
$$
The point $F$ lies outside the line. Let $G$ be the circumcentre of triangle $A D F$ and $H$ be the circumcentre of triangle $B E F$. Show that lines $G H$ and $F C$ are perpendicular.