MathDB
junior area chasing, 3 equal segments, 2 equilaterals (2023 May Olympiad L1 p3)

Source:

March 24, 2024
geometryareas

Problem Statement

On a straight line ā„“\ell there are four points, AA, BB, CC and DD in that order, such that AB=BC=CDAB=BC=CD. A point EE is chosen outside the straight line so that when drawing the segments EBEB and ECEC, an equilateral triangle EBCEBC is formed . Segments EAEA and EDED are drawn, and a point FF is chosen so that when drawing the segments FAFA and FEFE, an equilateral triangle FAEFAE is formed outside the triangle EADEAD. Finally, the lines EBEB and FAFA are drawn , which intersect at the point GG. If the area of triangle EBDEBD is 1010, calculate the area of triangle EFGEFG.