Chord of a circle
= Chord of a circle
{title2=$L=2\sqrt{r^2-d^2}$}
= Chord
{synonym}
A chord joins two points of a <circle> by a straight segment. If the circle has radius $r$ and the chord midpoint lies a distance $d$ from its center, the perpendicular bisector and <Pythagorean theorem> give the displayed length. The length exceeds that of an inscribed <equilateral triangle> precisely when $d<r/2$.