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midpoints and circumcircles

Source: 2021 SRMC P3

June 28, 2021
geometry

Problem Statement

In a triangle ABCABC, MM is the midpoint of the ABAB. A point B1B_1 is marked on ACAC such that CB=CB1CB=CB_1. Circle ω\omega and ω1\omega_1, the circumcircles of triangles ABCABC and BMB1BMB_1, respectively, intersect again at KK. Let QQ be the midpoint of the arc ACBACB on ω\omega. Let B1QB_1Q and BCBC intersect at EE. Prove that KCKC bisects B1EB_1E.
M. Kungozhin
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