An exploration of [url=http://mathani.tumblr.com/post/77482183135/two-circles-intersect-at-two-points-as-a-point] mathani [/url]'s post - "Two circles intersect at two points. As a point moves along the major arc of the smaller circle, the length of the formed chord in the larger circle remains the same."
A sketch that inspired this one [url=http://www.geogebratube.org/material/show/id/89395]here[/url].