Problem

Source: Romania TST 4 (All Geometry) 2010, Problem 2

Tags: Euler, geometry proposed, geometry



mavropnevma

25.08.2012 15:06

Let $ABC$ be a scalene triangle. The tangents at the perpendicular foot dropped from $A$ on the line $BC$ and the midpoint of the side $BC$ to the nine-point circle meet at the point $A'$\,; the points $B'$ and $C'$ are defined similarly. Prove that the lines $AA'$, $BB'$ and $CC'$ are concurrent. Gazeta Matematica