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Triangles that share an orthocentre

Source: Czech-Polish-Slovak 2004 Q5

April 28, 2013
geometryvectorcircumcirclegeometry unsolved

Problem Statement

Points K,L,MK,L,M on the sides AB,BC,CAAB,BC,CA respectively of a triangle ABCABC satisfy AKKB=BLLC=CMMA\frac{AK}{KB} = \frac{BL}{LC} = \frac{CM}{MA}. Show that the triangles ABCABC and KLMKLM have a common orthocenter if and only if △ABC\triangle ABC is equilateral.
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