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Equilateral triangle with ratio of regular pentagon

Source: Sharygin Finals 2017, Problem 9.1

August 3, 2017
ratiogeometryGolden Ratio

Problem Statement

Let ABCABC be a regular triangle. The line passing through the midpoint of ABAB and parallel to ACAC meets the minor arc ABAB of the circumcircle at point KK. Prove that the ratio AK:BKAK:BK is equal to the ratio of the side and the diagonal of a regular pentagon.
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