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4 lines in the plane

Source: Canada 1972, Problem 9

June 25, 2006
geometryparallelogram

Problem Statement

Four distinct lines L1,L2,L3,L4L_1,L_2,L_3,L_4 are given in the plane: L1L_1 and L2L_2 are respectively parallel to L3L_3 and L4L_4. Find the locus of a point moving so that the sum of its perpendicular distances from the four lines is constant.
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