Problem

Source:

Tags: geometry, geometry proposed, geometry unsolved



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.