The theorem of the chord angle says that the angle from a point on the circle to the ends of a chord of the same circle is constant. It is a consequence of the chord quadrilateral theorem, which states that opposing angles add to 180° in a quadrilateral with all corners on one circle.

 

Move C or D. The angles remain constant and add to 180°.

The reverse is also true. If the angle is constant, the points is on a circle.

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