The first theorem is the property theorem of tangent. This theorem is simple and not difficult to understand. Just remember: "crossing the center of the circle", "crossing the tangent point" and "perpendicular to each other".

The second theorem is the tangent theorem, which is often tested in the senior high school entrance examination. There are three main methods to judge tangency: definition method, distance method and theorem method. Theorem method is the most commonly used method, followed by distance method, and definition method is rarely used.

Here, when judging tangency, you only need to remember: "There is an intersection point, a radius, and it is vertical; No intersection, vertical, positive radius ". That is to say, the judgment of tangent is mainly based on these two types of questions, that is, the topic says that straight lines and circles have intersections, and straight lines and circles have no intersections.

The third theorem is the tangent length theorem. In this theorem, two tangents formed by the same intersection point are equal in length, and the connecting line between this intersection point and the center of the circle is the bisector of the included angle between the two tangents, so there is a pair of equal angles. When students do the corresponding exercises, they should see the tangent length in a conditioned way, and know that there are two equal groups, that is, the straight lines are equal and the angles are equal.

Tangent angle theorem of circle

The degree of the chord tangent angle is equal to half the degree of the central angle of the arc it cuts, and equal to the degree of the central angle of the arc it cuts. The angle formed by the intersection of the straight line tangent to the circle and the chord intersecting the circle in the circle is called the chord tangent angle.