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Iranian TST 2019, second exam, day 1, problem 2

Source: Iranian TST

April 11, 2019
TSTIranian TSTgeometryIran

Problem Statement

In a triangle ABCABC, ∠A\angle A is 60∘60^\circ. On sides ABAB and ACAC we make two equilateral triangles (outside the triangle ABCABC) ABKABK and ACLACL. CKCK and ABAB intersect at SS , ACAC and BLBL intersect at RR , BLBL and CKCK intersect at TT. Prove the radical centre of circumcircle of triangles BSK,CLRBSK, CLR and BTCBTC is on the median of vertex AA in triangle ABCABC. Proposed by Ali Zamani
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