Let H and I be the orthocenter and incenter, respectively, of an acute-angled triangle ABC. The circumcircle of the triangle BCI intersects the segment AB at the point P different from B. Let K be the projection of H onto AI and Q the reflection of P in K. Show that B, H and Q are collinear.Proposed by Mads Christensen, Denmark geometryincentercircumcirclegeometric transformationreflection