Problem #WSP-5659

Problem

Let \(H\) be the orthocenter of triangle \(\triangle ABC\) (i.e: the point where the three heights meet). Let \(D,E,F\) be three points on the circumcircle of \(\triangle ABC\) such that lines \(\overline{AD}, \overline{FC}, \overline{BE}\) are all parallel to each other. Then, let \(D',E',F'\) be obtained by reflecting \(D,E,F\) across \(BC,CA,AB\) respectively. Prove that the points \(H,D',E',F'\) all lie on the same circle.