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Arbitrary lines made by regular 13-gons concur

Source: Sharygin Finals 2017, Problem 8.7

August 4, 2017

geometryconcurrency

Problem Statement

Let

A_1A_2 \dots A_{13}

and

B_1B_2 \dots B_{13}

be two regular

13

-gons in the plane such that the points

B_1

and

A_{13}

coincide and lie on the segment

A_1B_{13}

, and both polygons lie in the same semiplane with respect to this segment. Prove that the lines

A_1A_9, B_{13}B_8

and

A_8B_9

are concurrent.