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A nice problem. Olympic VietNam 2007-2008 (New).

Source: Vietnam MO 2008, Problem 7

January 29, 2008
geometrycircumcircleanalytic geometrygraphing linesslopeparallelogramgeometric transformation

Problem Statement

Let AD AD is centroid of ABC ABC triangle. Let (d) (d) is the perpendicular line with AD AD. Let M M is a point on (d) (d). Let E,F E, F are midpoints of MB,MC MB, MC respectively. The line through point E E and perpendicular with (d) (d) meet AB AB at P P. The line through point F F and perpendicular with (d) (d) meet AC AC at Q Q. Let (d′) (d') is a line through point M M and perpendicular with PQ PQ. Prove (d′) (d') always pass a fixed point.
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