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Turkish MO 1995 P4

Source: Turkish Mathematical Olympiad 2nd Round 1995

September 30, 2006
ratiotrigonometrygeometry unsolvedgeometry

Problem Statement

In a triangle ABCABC with AB≠ACAB\neq AC, the internal and external bisectors of angle AA meet the line BCBC at DD and EE respectively. If the feet of the perpendiculars from a point FF on the circle with diameter DEDE to BC,CA,ABBC,CA,AB are K,L,MK,L,M, respectively, show that KL=KMKL=KM.
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