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Geometry about a triangle with <B=60

Source: ARO 2021 9.6

April 20, 2021
geometry

Problem Statement

Given is a non-isosceles triangle ABCABC with ∠ABC=60∘\angle ABC=60^{\circ}, and in its interior, a point TT is selected such that ∠ATC=∠BTC=∠BTA=120∘\angle ATC= \angle BTC=\angle BTA=120^{\circ}. Let MM the intersection point of the medians in ABCABC. Let TMTM intersect (ATC)(ATC) at KK. Find TM/MKTM/MK.
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