Problem

Source: 6th Iranian Geometry Olympiad (Advanced) P5

Tags: IGO, Iran, geometry, parabola



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