Problem

Source: 6th Iranian Geometry Olympiad (Advanced) P5

Tags: IGO, Iran, geometry, parabola



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