The chord angle theorem states that in an inscribed triangle (ABC) where A is the center of the circle and BC is a chord, and BDC is an inscribed triangle on the same chord, angle BDC must equal one half of angle BAC. Try changing the angle and moving point D and observe the theorem’s truth.

Note: the measure of angle BDC is being constantly recalculated as point D is dragged, but it doesn’t change because of this theorem.