Problem #PRU-58094

Problems Geometry Plane geometry Methods Circles Pigeonhole principle (angles and lengths) Connection between the arc length, the angle, and the chord Central angle. Arc length and circumference Pigeonhole principle
 13–15  4.0

Problem

Several chords are drawn through a unit circle. Prove that if each diameter intersects with no more than \(k\) chords, then the total length of all the chords is less than \(\pi k\).