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<ABC wanted if B, T, E are collinear and <ATB = <BTC = 120^o

Source: 2021 Sharygin Finals grade IX p3

August 1, 2021
anglesgeometryequal angles

Problem Statement

Let ABCABC be an acute-angled scalene triangle and TT be a point inside it such that ∠ATB=∠BTC=120o\angle ATB = \angle BTC = 120^o. A circle centered at point EE passes through the midpoints of the sides of ABCABC. For B,T,EB, T, E collinear, find angle ABCABC.
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