Let AA1 and BB1 be the altitudes of an acute-angled, non-isosceles triangle ABC. Also, let A0 and B0 be the midpoints of its sides BC and CA, respectively. The line A1B1 intersects the line A0B0 at a point C′. Prove that the line CC′ is perpendicular to the Euler line of the triangle ABC (this is the line that joins the orthocenter and the circumcenter of the triangle ABC). EulergeometrycircumcircleLaTeXparallelogramprojective geometryperpendicular bisector