What theorems do you need to master in high school mathematics competition?
As far as geometry is concerned, problems are mainly divided into two categories: the first category, combinatorial problems, points * * * lines, lines * * * points and points * * * circles. From a practical point of view, Ceva Theorem and Menelaus Theorem belong to basic knowledge and require higher requirements: in the sense of central perspective, Ceva Theorem and Menelaus Theorem are unified into Desargues Theorem. Menelaus theorem is unified into harmonic point sequence, root axis theorem and Pascal theorem. In reverse evolution, the point * * * line and the point * * * circle are unified. For * * * circle, there are circle power theorem and Ptolemy theorem, and the method of inferring * * * circle from the angle belongs to basic common sense. The second category is geometric invariance and geometric invariance of special graphics. There are mainly circles and triangles.