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,
If any side is extended along a straight line, the exterior angle formed is equal to the opposite, interior angle of the quadrilateral.
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,
The perpendicular bisector of every chord on a circle passes through the circle center.