IGO 2019 A5

Let points $A, B$ and $C$ lie on the parabola $\Delta$ such that the point $H$ , orthocenter of triangle $ABC$ , coincides with the focus of parabola $\Delta$ . Prove that by changing the position of points $A, B$ and $C$ on $\Delta$ so that the orthocenter remain at $H$ , inradius of triangle $ABC$ remains unchanged.

Proposed by Mahdi Etesamifard