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5 triangles with equal areas in a convex pentagon

Source: Mexican Mathematical Olympiad 1995 OMM P5

July 28, 2018
geometrypentagonareas

Problem Statement

ABCDEABCDE is a convex pentagon such that the triangles ABC,BCD,CDE,DEAABC, BCD, CDE, DEA and EABEAB have equal areas. Show that (1/4)(1/4) area (ABCDE)<(ABCDE) < area (ABC)<(1/3)(ABC) < (1/3) area (ABCDE)(ABCDE).
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