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Angle bisectors

Source: Iran MO 3rd round 2016 finals - Geometry P3

September 5, 2016
geometryangle bisectorIran

Problem Statement

Given triangle △ABC\triangle ABC and let D,E,FD,E,F be the foot of angle bisectors of A,B,CA,B,C ,respectively. M,NM,N lie on EFEF such that AM=ANAM=AN. Let HH be the foot of AA-altitude on BCBC. Points K,LK,L lie on EFEF such that triangles △AKL,△HMN\triangle AKL, \triangle HMN are correspondingly similiar (with the given order of vertices) such that AK∦HMAK \not\parallel HM and AK∦HNAK \not\parallel HN.
Show that: DK=DLDK=DL
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