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trisection of diagonal by perp. in # with 60^o (2010 VWO Flanders MO p3)

Source:

August 7, 2020
geometryparallelolgramratiotrisection

Problem Statement

A parallelogram with an angle of 60o60^o has aa as the longest side and a shortest side bb. Let's take the perpendiculars down from the vertices of the obtuse angles to the longest diagonal, then it is divided into three equal parts. Determine the ratio ab\frac{a}{b}.