MathDB

Let

A_0A_1A_2A_3A_4A_5

be a convex hexagon inscribed in a circle. Define the points

A_0'

A_2'

A_4'

on the circle, such that A_0A_0' \parallel A_2A_4, A_2A_2' \parallel A_4A_0, A_4A_4' \parallel A_2A_0 . Let the lines

A_0'A_3

and

A_2A_4

intersect in

A_3'

, the lines

A_2'A_5

and

A_0A_4

intersect in

A_5'

and the lines

A_4'A_1

and

A_0A_2

intersect in

A_1'

. Prove that if the lines

A_0A_3

A_1A_4

and

A_2A_5

are concurrent then the lines

A_0A_3'

A_4A_1'

and

A_2A_5'

are also concurrent.

Problem Statement