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AO bisects EF, midpoint of altitude, circumcenter related

Source: 2021 Saudi Arabia Training Lists p20 https://artofproblemsolving.com/community/c2758131_2021_saudi_arabia_training_tests

January 6, 2022
geometrybisects segmentcircumcircle

Problem Statement

Let ABCABC be an acute, non-isosceles triangle with altitude ADAD (DāˆˆBCD \in BC), MM is the midpoint of ADAD and OO is the circumcenter. Line AOAO meets BCBC at KK and circle of center KK, radius KAKA cuts AB,ACAB,AC at E,FE, F respectively. Prove that AOAO bisects EFEF.
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