MathDB
Xvii cono sur - peru tst 2006.

Source: Spanish Communities

April 4, 2006
EulergeometrycircumcircleLaTeXparallelogramprojective geometryperpendicular bisector

Problem Statement

Let AA1AA_1 and BB1BB_1 be the altitudes of an acute-angled, non-isosceles triangle ABCABC. Also, let A0A_0 and B0B_0 be the midpoints of its sides BCBC and CACA, respectively. The line A1B1A_1B_1 intersects the line A0B0A_0B_0 at a point C′C'. Prove that the line CC′CC' is perpendicular to the Euler line of the triangle ABCABC (this is the line that joins the orthocenter and the circumcenter of the triangle ABCABC).
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