Question 184
Let $ABC$ and $DEF$ be triangles with the same circumcircle centred at $O$ and the same orthocentre $H \neq O$. The Simson lines of $D, E, F$ with respect to triangle $ABC$ form a non-degenerate triangle $\triangle$. Prove that the orthocentre of $\triangle$ lies on the circle on diameter $OH$.
**Note.** Assume that $A, F, B, D, C, E$ form, in order around the circle, the vertex set of a non-degenerate convex hexagon.
**Note.** Assume that $A, F, B, D, C, E$ form, in order around the circle, the vertex set of a non-degenerate convex hexagon.