The region between two Concentric circles of different Radii is called an Annulus.
Given two concentric circles with Radii and , what is the probability that a chord chosen at random from the outer circle will cut across the inner circle? Depending on how the ``random'' Chord is chosen, 1/2, 1/3, or 1/4 could all be correct answers.
Given an arbitrary Chord to the larger of two concentric Circles centered on , the distance between inner and outer intersections is equal on both sides . To prove this, take the Perpendicular to passing through and crossing at . By symmetry, it must be true that and are equal. Similarly, and must be equal. Therefore, equals . Incidentally, this is also true for Homeoids, but the proof is nontrivial.
See also Annulus