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7 regions of equal area - JBMO Shortlist

Source:

October 30, 2010
geometrygeometry proposed

Problem Statement

Let ABCABC be a triangle. Find all the triangles XYZXYZ with vertices inside triangle ABCABC such that XY,YZ,ZXXY,YZ,ZX and six non-intersecting segments from the following AX,AY,AZ,BX,BY,BZ,CX,CY,CZAX, AY, AZ, BX, BY, BZ, CX, CY, CZ divide the triangle ABCABC into seven regions with equal areas.
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