The new definition of the final question is a unique test question with new questions and high flexibility. It requires students to learn new knowledge on the spot and use the knowledge they have learned to solve new problems. Four major difficulties: 1. Cannot understand the que

New definition The final question is a unique test question with new questions and high flexibility. It requires students to learn new knowledge on site

and use the knowledge they have learned to solve new problems.

Four major difficulties

① Can't understand the question and can't refine it

② Can’t transfer knowledge and stay on the surface of the problem;

③ Can’t analyze the problem, don’t know how to start, can’t find a breakthrough to solve the problem;

④ Dynamic geometry, can’t imagine how the graphics move and change.

solution Question steps

① Quickly review the question and extract hidden information from known information;

② Convert the new definition language into the learned mathematical symbol language or mathematical model;

③ Don’t rush to solve the problem first, but first understand the essence of the problem and find the solution Breakthrough in the question;

④ Draw pictures, combine numbers and shapes with , and intuitively understand the investigated problems and the changing rules of graphic movement;

⑤ Answer the questions according to the requirements, pay attention to whether the critical point position can be taken, etc.

Definition: Point P is inside or on the side of △ABC For points on (except vertices), among △PAB, △PBC, and △PCA, if at least one triangle is similar to △ABC, then point P is said to be a self-similar point of △ABC. For example: As shown in Figure 1, point P is inside △ABC, ∠PBC=∠A, ∠PCB=∠ABC, then △BCP∽△ABC, so point P is the self-similar point of △ABC. Please use the knowledge you have learned and combine the above materials to solve the following problems: