Scene 1: Encounter a string. What is a string? According to the definition, the line segment connecting any two points on a circle is called a chord, and the chord passing through the center of the circle is called a diameter, which is the longest chord in a circle. When the knowledge of string appears in the topic of circle, we need to quickly associate some theorems and properties related to string, such as vertical diameter theorem, chord center distance, pythagorean theorem and so on.
The second scene: encounter diameter. Diameter is defined as a straight line connecting two points on the circumference and passing through the center of the circle. When the condition of diameter appears, we should also quickly associate the properties such as central angle and circumferential angle, and then construct isosceles triangle, right triangle and other graphics to solve the following problems.
The third scene: meet a tangent. The definition of tangent is: if there is only one intersection point between a straight line and a circle, then this straight line is the tangent of the circle. Generally, if the topic is given a tangent line, we can consider adding the radius of the tangent point, and then connect the center of the circle with the tangent point, and construct a right-angled or right-angled triangle by using the properties and theorems of the tangent line, so as to solve some corner relations by using Pythagorean theorem.
The fourth scene is to meet intersecting tangents, similar to the tangents above. In this special case, we often consider connecting the center of the circle with the tangent point, or connecting the center of the circle with a point outside the circle, or connecting two tangent points as needed. Through these different operations, we can get some special triangle and corner relations, such as congruence, similarity, verticality, corner relations and so on, which is very useful.
Fifth, the triangle inscribed circle. Generally, when we encounter this kind of scene, we will make the following auxiliary lines: passing through the center of the circle as the vertical line segment of each side of the triangle or connecting the center of the circle to the vertex of each triangle. The idea is also to construct a special angular relationship and triangle. There are two very important properties that must be clearly remembered: 1, the line from the center of the circle to the vertex of the triangle is the bisector; 2. The distance from the center of the circle to the three sides of the triangle is equal.
Sixth, the triangle circumscribes the circle. If this is the case, we usually construct a diameter first, and then construct a special relationship between triangle and angle according to some known conditions of the topic, so as to solve the following two problems.