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Concyclic 6 points with simson lines

Source: 2018 Korea Winter Program Practice Test 1 #3

January 7, 2018

Simson lineConcyclicgeometry

Problem Statement

Denote

A_{DE}

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

A_{FD}A_{DE}

B_{DE}B_{EF}

C_{EF}C_{FD}

, and the three points determined by the lines

D_{CA}D_{AB}

E_{AB}E_{BC}

F_{BC}F_{CA}

are concyclic.