MathDB

1

Part of 2000 Singapore Senior Math Olympiad

Problems(1)

6 triangles with equal areas

Source: Singapore Senior Math Olympiad 2000 2nd Round p1 SMO

4/4/2020
In △ABC\vartriangle ABC, the points D,ED, E and FF lie on AB,BCAB, BC and CACA respectively. The line segments AE,BFAE, BF and CDCD meet at the point GG. Suppose that the area of each of △BGD,△ECG\vartriangle BGD, \vartriangle ECG and △GFA\vartriangle GFA is 11 cm2^2. Prove that the area of each of △BEG,△GCF\vartriangle BEG, \vartriangle GCF and △ADG\vartriangle ADG is also 11 cm2^2. https://cdn.artofproblemsolving.com/attachments/e/7/ec090135bd2e47a9681d767bb984797d87218c.png
triangle areaequal areasareasgeometry