Let $ABC$ be an acute-angled scalene triangle and $T$ be a point inside it such that $\angle ATB = \angle BTC = 120^o$. A circle centered at point $E$ passes through the midpoints of the sides of $ABC$. For $B, T, E$ collinear, find angle $ABC$.
Source: 2021 Sharygin Finals grade IX p3
Tags: angles, geometry, equal angles
Let $ABC$ be an acute-angled scalene triangle and $T$ be a point inside it such that $\angle ATB = \angle BTC = 120^o$. A circle centered at point $E$ passes through the midpoints of the sides of $ABC$. For $B, T, E$ collinear, find angle $ABC$.