MathDB

3

Part of 2022 Sharygin Geometry Olympiad

Problems(1)

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

Source: 2022 Sharygin CR p3

3/6/2022
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
geometryequal segmentsright triangle