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Concyclicity with symmedian

Source: 2023 Israel TST Test 5 P2

March 23, 2023
geometryTSTsymmedianincenter

Problem Statement

Let ABCABC be an isosceles triangle, AB=ACAB=AC inscribed in a circle ω\omega. The BB-symmedian intersects ω\omega again at DD. The circle through C,DC,D and tangent to BCBC and the circle through A,DA,D and tangent to CDCD intersect at points D,XD,X. The incenter of ABCABC is denoted II. Prove that B,C,I,XB,C,I,X are concyclic.
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