Vertical diameter theorem: perpendicular to the diameter of a chord, bisect the chord and bisect the two arcs opposite to the chord.

Central Angle Theorem: In the same circle or equal circle, there are two central angles, two chords, the chord center distance of two chords, and two arcs. If one of these four quantities is equal, so are the other three quantities.

Theorem of circle angle: the circle angle of an arc is equal to half the central angle of this arc.

Inference of the fillet theorem: (1) The fillet subtended by the diameter or semicircle is a right angle; (2) The chord subtended by the circumferential angle of 90 degrees is the diameter, and the arc subtended is the semicircle; (3) The circumferential angles of the same arc or equal arc are equal.

Chord tangent angle theorem: the chord tangent angle is equal to the circumferential angle of the arc it clamps.

Chord intersection theorem: two chords intersect, and the product of two line segments divided by the intersection point is equal.