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FL = CL + LD wanted, altitude of right triangle ABC, equilaterals AED, CFD

Source: 2022 Sharygin CR p3

March 6, 2022
geometryequal segmentsright triangle

Problem Statement

Let CDCD be an altitude of right-angled triangle ABCABC with ∠C=90\angle C = 90. Regular trianglesAED AED and CFDCFD are such that EE lies on the same side from ABAB as CC, and FF lies on the same side from CDCD as BB. The line EFEF meets ACAC at LL. Prove that FL=CL+LDFL = CL + LD
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