Problem #PRU-58097

Problems Geometry Plane geometry Circles Central angle. Arc length and circumference Plane transformations Projection onto a line Orthogonal projection Methods Pigeonhole principle Pigeonhole principle (angles and lengths)
 13–16  3.0

Problem

Several circles, whose total length of circumferences is 10, are placed inside a square of side 1. Prove that there will always be some straight line that crosses at least four of the circles.