Τετάρτη, 11 Οκτωβρίου 2017

2000 JBMO Shortlist 17


A triangle ${ABC}$ is given. Find all the pairs of points ${X, Y}$ so that ${X}$ is on the sides of the triangle, ${Y}$ is inside the triangle, and four non-intersecting segments from the set ${ \{ XY,AX, AY,BX,BY,CX,CY \} }$ divide the triangle ${ABC}$ into four triangles with equal areas.

proposed in aops here

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