Problem

Source: Swiss Math Olympiad 2010 - final round, problem 2

Tags: geometry, geometry proposed



Let $ \triangle{ABC}$ be a triangle with $ AB\not=AC$. The incircle with centre $ I$ touches $ BC$, $ CA$, $ AB$ at $ D$, $ E$, $ F$, respectively. Furthermore let $ M$ the midpoint of $ EF$ and $ AD$ intersect the incircle at $ P\not=D$. Show that $ PMID$ ist cyclic.