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Let S be a finite set of geometric objects partitioned into classes or colors. A subset S′⊆ S is said to be balanced if S′ contains the same amount of elements of S from each of the colors. We study several problems on partitioning 3-colored sets of points and lines in the plane into two balanced subsets:(a) We prove that for every 3-colored arrangement of lines there exists a segment that intersects exactly one line of each color, and that when there are 2 m lines of each color, there is a segment intercepting m lines of each color.(b) Given n red points, n blue points and n green points on any closed Jordan curve γ, we show that for every integer k with 0≤ k≤ n there is a pair of disjoint intervals on γ whose union contains exactly k points of each color.(c) Given a set S of n red points, n blue points and n green points in the integer lattice satisfying certain constraints, there exist two rays with common apex, one vertical …