Problem

Source: ELMO 2020 P3

Tags: perpendicular bisector, orthocenter



Janabel has a device that, when given two distinct points $U$ and $V$ in the plane, draws the perpendicular bisector of $UV$. Show that if three lines forming a triangle are drawn, Janabel can mark the orthocenter of the triangle using this device, a pencil, and no other tools. Proposed by Fedir Yudin.