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Metric relation in regular 2018- gon

Source: Latvian TST for Baltic Way 2019, Problem 11

June 4, 2020
geometrycircumcircle

Problem Statement

Let A1A2...A2018A_1A_2...A_{2018} be regular 20182018-gon. Radius of it's circumcircle is RR. Prove that: A1A1008−A1A1006+A1A1004−A1A1002+...+A1A4−A1A2=RA_1A_{1008}-A_1A_{1006}+A_1A_{1004}-A_1A_{1002} + ... + A_1A_4 -A_1A_2=R
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