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Circumcircle is tangent to another incircle

Source: Indonesian Mathematics Olympiad 2011, Day 2, Problem 8

September 14, 2011
geometrycircumcirclegeometry unsolved

Problem Statement

Given a triangle ABCABC. Its incircle is tangent to BC,CA,ABBC, CA, AB at D,E,FD, E, F respectively. Let K,LK, L be points on CA,ABCA, AB respectively such that K≠A≠L,∠EDK=∠ADE,∠FDL=∠ADFK \neq A \neq L, \angle EDK = \angle ADE, \angle FDL = \angle ADF. Prove that the circumcircle of AKLAKL is tangent to the incircle of ABCABC.
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