Problem

Source: 2018 Korea Winter Program Practice Test 1 #3

Tags: Simson line, Concyclic, geometry



Denote ADE by the foot of perpendicular line from A to line DE. Given concyclic points A,B,C,D,E,F, show that the three points determined by the lines AFDADE , BDEBEF , CEFCFD, and the three points determined by the lines DCADAB , EABEBC , FBCFCA are concyclic.