The triangle $ABC$ is drawn on the board such that $AB + AC = 2BC$. The bisectors $AL_1, BL_2, CL_3$ were drawn in this triangle, after which everything except the points $L_1, L_2, L_3$ was erased. Use a compass and a ruler to reconstruct triangle $ABC$.
Problem
Source: 2012 XV All-Ukrainian Tournament of Young Mathematicians named after M. Y. Yadrenko, Qualifying p2
Tags: geometry, construction, angle bisector, Ukrainian TYM