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Four concyclic points (BxMO 2022, Problem 3)

Source: BxMO 2022, Problem 3

May 1, 2022
geometryBxMO

Problem Statement

Let ABCABC be a scalene acute triangle. Let B1B_1 be the point on ray [AC[AC such that ∣AB1∣=∣BB1∣|AB_1|=|BB_1|. Let C1C_1 be the point on ray [AB[AB such that ∣AC1∣=∣CC1∣|AC_1|=|CC_1|. Let B2B_2 and C2C_2 be the points on line BCBC such that ∣AB2∣=∣CB2∣|AB_2|=|CB_2| and ∣BC2∣=∣AC2∣|BC_2|=|AC_2|. Prove that B1B_1, C1C_1, B2B_2, C2C_2 are concyclic.
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