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triangle construction, AB + AC = 2BC, feet of angle bisectors

Source: 2012 XV All-Ukrainian Tournament of Young Mathematicians named after M. Y. Yadrenko, Qualifying p2

May 11, 2021
geometryconstructionangle bisectorUkrainian TYM

Problem Statement

The triangle ABCABC is drawn on the board such that AB+AC=2BCAB + AC = 2BC. The bisectors AL1,BL2,CL3AL_1, BL_2, CL_3 were drawn in this triangle, after which everything except the points L1,L2,L3L_1, L_2, L_3 was erased. Use a compass and a ruler to reconstruct triangle ABCABC.
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