SHARYGIN 2011 Problem 14

In triangle $ABC$ , the altitude and the median from vertex $A$ form (together with line $BC$ ) a triangle such that the bisectrix of angle $A$ is the median; the altitude and the median from vertex $B$ form (together with line AC) a triangle such that the bisectrix of angle $B$ is the bisectrix. Find the ratio of sides for triangle $ABC$ .