In a quadrilateral inscribed in a circle, the sum of opposite interior angles is 180 degrees.
Notes: 1. Put another way, for a quadrilateral inscribed in a circle, [i]If any side is extended along a straight line, the exterior angle formed is equal to the opposite, interior angle of the quadrilateral.[/i] 2. If we begin with the three points A, B, C, and construct the circumscribing circle of triangle ABC, wherever we place D on the circle, the perpendicular bisectors of the new sides CD, BD and diagonal AD, must all pass through O. That is, the perpendicular bisector of any two points lying on a circle pass through the circle center, or, [i]The perpendicular bisector of every chord on a circle passes through the circle center.[/i]