This is pretty: If you choose n > 1 equally spaced points on a unit circle and connect one of them to each of the others, the product of the lengths of these chords equals n.

(Andre P. Mazzoleni and Samuel Shan-Pu Shen, “The Product of Chord Lengths of a Circle,” Mathematics Magazine 68:1 [February 1995], 59-60.)

(Demonstration by Jay Warendorff.)