MathDB

20

Part of 2021 Saudi Arabia Training Tests

Problems(1)

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

1/6/2022
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.
geometrybisects segmentcircumcircle