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if 3 of 4 intersections are collinear then all 4 are, in a cyclic hexagon

Source: 2015 Sharygin Geometry Olympiad Correspondence Round P18

August 2, 2018

geometrycollinearhexagon

Problem Statement

Let

ABCDEF

be a cyclic hexagon, points

K, L, M, N

be the common points of lines

AB

and

CD

AC

and

BD

AF

and

DE

AE

and

DF

respectively. Prove that if three of these points are collinear then the fourth point lies on the same line.