The angle formed by the vertex on the circle, one side intersecting the circle and the other side tangent to the circle is called the tangent angle. (Chord tangent angle is the angle between tangent and chord. )
Inference: If the arc enclosed by two chord tangent angles is equal, then the two chord tangent angles are also equal.
2. Tangent length theorem: the tangent lengths of two tangents drawn from a point outside the circle are equal, and the connecting line between the center of the circle and this point bisects the included angle of the two tangents. 3. Circle Power Theorem (1) Intersecting chord theorem: The product of two intersecting chords divided by the intersection point in a circle is equal. Draw two chords by a point on the circle, and the product of two line segments divided by this point is equal. Inference: If the chord intersects the diameter vertically, then half of the chord is the proportional average of the two line segments formed by its diameter. (2) Secant theorem: the tangent and secant drawn from a point outside the circle, and the length of the tangent is the proportional average of the lengths of the two lines intersecting the circle at that point. This is a cyclic power theorem.
Inference:
Draw two secants of a circle from a point outside the circle, and the product of the lengths of the two lines from that point to the intersection of each secant and the circle is equal.
(3) Secant theorem: the product of the distance from a point outside the circle to the intersection of each secant and the circle is equal.