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DE = r wanted, inscribed isosceles ABC, equilateral BCD

Source: 1985 Swedish Mathematical Competition p3

March 28, 2021
geometryisoscelesEquilateral

Problem Statement

Points A,B,CA,B,C with AB=BCAB = BC are given on a circle with radius rr, and DD is a point inside the circle such that the triangle BCDBCD is equilateral. The line ADAD meets the circle again at EE. Show that DE=rDE = r.
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