The five cases of invisible circle are diagonal complementarity and four-point * * * circle; Set the chord and angle, and point on the circle; Fixed point and fixed length. The application of invisible circle is a common topic in senior high school entrance examination. This kind of problem does not directly give information about the circle in the conditions, but we can finally solve it by using the knowledge of the circle through analysis and transformation.

This kind of topic is unique and comprehensive. It transforms the complex problem of polygon angle finding into the problem of circle angle finding, which embodies the mathematical idea of reduction. The key to deal with this kind of topic is whether we can find out the "invisible circle".

Test situation analysis:

Circle is one of the most important knowledge points and one of the difficulties in junior high school mathematical geometry. Common knowledge points are: the positional relationship between a straight line and a circle; The positional relationship between circles (some areas of this knowledge point have been deleted); Vertical diameter theorem; The relationship between chord, arc, central angle and circumferential angle; Arc length formula; Sector area formula, etc.

In addition to the problem of area in small questions and the problem of proof in solving problems, various properties of circles are often investigated in the form of finale questions. In recent years, the "invisible circle" has also been favored by questioners, which can solve the most valuable problems and other related types of problems. The "invisible circle" model has two basic model diagrams.