On the base $BC$ of the isosceles triangle $ABC$ chose a point $D$ and in each of the triangles $ABD$ and $ACD$ inscribe a circle. Then everything was wiped, leaving only two circles. It is known from which side of their line of centers the apex $A$ is located . Use a compass and ruler to restore the triangle $ABC$ , if we know that : a) $AD$ is angle bisector, b) $AD$ is median.
Problem
Source: 2019 XXII All-Ukrainian Tournament of Young Mathematicians named after M. Y. Yadrenko, Qualifying p9
Tags: construction, isosceles, inradius, geometry, Ukrainian TYM