MathDB

5

Part of 2009 Regional Olympiad of Mexico Center Zone

Problems(1)

AN _|_ NM wanted, AE _|_ BE, AF _|_ CF, altitude, midpoints

Source: Mathematics Regional Olympiad of Mexico Center Zone 2009 P5

11/10/2021
Let ABCABC be a triangle and let DD be the foot of the altitude from AA. Let points EE and FF on a line through DD such that AEAE is perpendicular to BEBE, AFAF is perpendicular to CFCF, where EE and FF are points other than the point DD. Let MM and NN be the midpoints of BCBC and EFEF, respectively. Prove that ANAN is perpendicular to NMNM.
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