Problem #PRU-34905

Problems Geometry Plane geometry Area Area of a trapezium Area ratio Area Ratio Methods Pigeonhole principle Pigeonhole principle (finite number of poits, lines etc.) Quadrilateral Parallelogram Special cases Rectangles and squares. Criteria and properties
 13–14  4.0

Problem

9 straight lines each divide a square into two quadrilaterals, with their areas having a ratio of \(2:3\). Prove that at least three of the nine lines pass through the same point.