MathDB
easy geometry

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May 30, 2009
geometrygeometry proposed

Problem Statement

Let ABC ABC be an acute triangle, AD,BE,CZ AD,BE,CZ its altitudes and H H its orthocenter. Let AI,AΘ AI,A \Theta be the internal and external bisectors of angle A A. Let M,N M,N be the midpoints of BC,AH BC,AH, respectively. Prove that: (a) MNMN is perpendicular to EZEZ (b) if MN MN cuts the segments AI,AΘ AI,A \Theta at the points K,L K,L, then KL\equal{}AH
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