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computational, isosceles inscribed in semicircle, equilaterals

Source: OLCOMA Costa Rica National Olympiad, Final Round, 2014 3.4

October 1, 2021
semicircleequilateralsisoscelesgeometry

Problem Statement

Consider the isosceles triangle ABCABC inscribed in the semicircle of radius r r. If the △BCD\vartriangle BCD and △CAE\vartriangle CAE are equilateral, determine the altitude of △DEC\vartriangle DEC on the side DEDE in terms of r r. https://cdn.artofproblemsolving.com/attachments/6/3/772ff9a1fd91e9fa7a7e45ef788eec7a1ba48e.png
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