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IMOC 2020 G3 (circumcenter of OM_BM_C lies on Euler line of BIC)

Source: https://artofproblemsolving.com/community/c6h2254883p17398793

September 1, 2020
geometrycircumcircleEuler Lineincenter

Problem Statement

Triangle ABCABC has incenter II and circumcenter OO. AI,BI,CIAI, BI, CI intersect the circumcircle of ABCABC again at MA,MB,MCM_A, M_B, M_C, respectively. Show that the Euler line of BICBIC passes through the circumcenter of OMBMCOM_BM_C.
(houkai)
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