Question 42
Let $A B C D E F G H I L M N$ be a regular dodecagon. Let $P$ be the point of intersection of the diagonals $A F$ and $D H$. Let $S$ be the circle through $A$ and $H$, congruent to the circle circumscribed about the dodecagon and distinct from it. Prove that:
(a) $P$ belongs to $S$;
(b) the centre of $S$ belongs to the diagonal $H N$;
(c) the length of $P E$ is equal to the side of the dodecagon.
(a) $P$ belongs to $S$;
(b) the centre of $S$ belongs to the diagonal $H N$;
(c) the length of $P E$ is equal to the side of the dodecagon.