1, the position and function of teaching materials.

The teaching of circle plays an important role in plane geometry and even the whole middle school teaching, and the positional relationship between point and circle is widely used. It is a comprehensive application of junior high school geometry, which is based on learning the related concepts of circle, paving the way for the positional relationship between straight line and circle.

2. Play an important role in solving problems and proving geometry in the future.

Analysis of learning situation

On the basis of Grade One and Grade Two, Grade Three students have certain analytical power and inductive power, and according to their own characteristics, combined with the problems in real life, combined with the learning materials suitable for students of this class, they focus on stimulating students' curiosity and let them really understand the content of this lesson. Through the reflection on the research process, we can further strengthen our understanding of the idea of classification and transformation.

The main obstacle for students to form knowledge in this class is ruler drawing.

Teaching objectives

1 Knowledge and skills: Understanding the positional relationship between a point and a circle is determined by the distance between the point and the center of the circle.

main points

Close to the circle, understand that three points that are not on the same straight line determine a circle;

Understand the concepts of circumscribed circle of triangle, outer center of triangle and inscribed triangle of circle.

The circumscribed circle of a triangle has mastered the method of making a circle at three points that are not on the same line.

2. Process method: By intuitively feeling the three positional relationships between the point and the circle from the graph. Students begin to draw pictures and judge the position relationship between points and circles in theory.

3. Emotional attitudes and values: In solving problems, teachers create situations to introduce new lessons, start with observing materials, ask questions, and let students combine what they have learned, abstract them into geometric figures, and then express them. Let students feel the three positional relationships between the point and the circle in real life, which will help students abstract practical problems into mathematical models.

Teaching emphases and difficulties

Judge the positional relationship between a point and a circle, understand that the circle is determined by three points on a straight line, and master the method of making a circle with three points that are not on the same straight line.

teaching process

Teaching link

Teachers' activities

The presupposition of students' behavior

Design intent

First, the position of the point and the three positional relationships of the circle

Second, how many points can determine a circle?

Three. common

Four. abstract

Verb (short for verb) homework

Intuitively feel the three positional relationships between points and circles from the graph.

Tip: The key to drawing this circle is to find the center of the circle. Draw a circle that passes through point A and point B at the same time.

Practical inquiry

Thinking: If there are three lines, can you still draw a circle? why

Students can find three positional relationships between a point and a circle.

Students will find it difficult to draw a circle after a point, after 2: 03.

Intuitive perception helps students understand knowledge.

Train students to find key points when solving problems.

Cultivate students' understanding of classification and transformation.

blackboard-writing design

First, the position of the point and the three positional relationships of the circle

Let the radius of ⊙O be r and the distance from the point to the center of the circle be d, then there is

Dr. Point is outside the circle.

Second, how many points can determine a circle?

Three points that are not on the same straight line determine a circle.

Third, summary.

We already know that a circle can be drawn through the three vertices of a triangle, and only one can be drawn. A circle passing through the three vertices of a triangle is called the circumscribed circle of the triangle. The center of the circumscribed circle of a triangle is called the epicenter of the triangle. This triangle is called the inscribed triangle of this circle. The outer center of a triangle is the intersection of perpendicular bisector of three sides of the triangle.

The knowledge point of finding the angle with known trigonometric function value in senior one mathematics 1) Mystery: in the closed interval.

Meet the condition sinx=a(- 1? Answer? The angle x of 1) is called the arcsine of the real number A, and is denoted as arcsina, that is, x=arcsina, where x?

, and a = sinx

Note that the arcsine represents an angle with a sine value of A and an angle of in.

Within (-1? Answer? 1)。

(2) anti-cosine: in the closed interval

, in line with the conditions cosx=a(- 1? Answer? The angle x of 1) is called the anti-cosine of the real number a, and is denoted as arccosa, that is, x=arccosa, where x? [0,? ], and a=cosx.

(3) arc tangent: in the open interval

Within, the angle x that satisfies the condition tanx=a(a is a real number) is called the arctangent of real number a, and is denoted as arctana, that is, x=arctana, where x?

a=tanx。

Properties of inverse trigonometric functions;

( 1)sin(arcsina)= a(- 1？ Answer? 1)，cos(arccosa)=a(- 1？ Answer? 1),

tan(arctana)= a；

(2)arcsin(-a)=-arcsina，arccos(-a)=？ -arccosa，arctan(-a)=-arctana；

(3)arcsina+arccosa=

;

(4)arcsin(sinx)=x, only if X is

Internal establishment; Similarly, arccos(cosx)=x, only if x is in the closed interval [0,? ] established.

Steps to find the angle with known trigonometric function values:

(1) Determine the quadrant where the terminal edge of the angle is located (or the coordinate axis where the terminal edge is located) by the sign of the known trigonometric function value;

(2) If the function value is positive, first find the corresponding acute angle? 1, if the function value is negative, first find the acute angle corresponding to its absolute value? 1;

(3) According to the quadrant of the angle, 0~2 is obtained by the inductive formula. If the angle suitable for the condition is in the second quadrant, what is it? -? 1; If the right angle is in the third quadrant, what is it? +? 1; In the fourth quadrant, so it's 2? -? 1; What if it is -2? In the fourth frame, the angle to 0 is -0. 1, in the third quadrant is-? +? 1, in the second quadrant is-? -? 1;