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Authoritative PPT Summary
"Positional Relationship between Points and Circles" Circle PPT Courseware 2
teaching objectives
knowledge and abilities
Understand that the positional relationship between a point and a circle is determined by the distance from the point to the center of the circle.
Understand that three points that are not on the same straight line determine a circle.
Be able to draw the circumcircle of a triangle and be familiar with related concepts.
Process and Method
Experience the process of exploring the positional relationship between points and circles, and experience the mathematical ideas of mathematical classification thinking.
small exercise
1. A is standing in the center of the classroom. If the distance between B and A is 3m, where should B stand? How many locations are there? Please explain by drawing a picture.
2. A stands in the center of the classroom. If the distance between B and A is required to be 3m, and the distance between B and C is 2m, then where should B stand? How many locations are there?
3． Now it is required that the distance between B and A is 3m, and the distance between B and C is 2m. So where should B stand? How many locations are there?
Knowledge points
Countless circles can be drawn through a given point.
Countless circles can be drawn through two known points.
A circle can be drawn through three points that are not on the same straight line, and only one circle can be drawn.
proof by contradiction
It is assumed that the conclusion of a proposition is not established, and a contradiction is derived through reasoning. Based on the contradiction, it is determined that the assumption is incorrect, and the original proposition is established. This method is called proof by contradiction.
The circumcenter of an acute triangle is inside the triangle.
The circumcenter of a right triangle is at the midpoint of the hypotenuse of the right triangle.
The circumcenter of an obtuse triangle is outside the triangle.
Three points determine the circle
Countless circles can be drawn through a given point.
Countless circles can be drawn through two known points.
A circle can be drawn through three points that are not on the same straight line, and only one circle can be drawn.
Practice in class
1. Decide whether the following statements are correct
(1) Any triangle must have a circumscribed circle ( )
(2) Any circle has and has only one inscribed triangle ( )
(3) A circle can be determined through three points ( )
(4) The distance from the circumcenter of the triangle to each vertex of the triangle is equal ( )
2. If the circumcenter of a triangle is on one side, the shape of the triangle is ( )
A. Acute triangle B. right triangle
C. Obtuse triangle D. isosceles triangle
3． The radius of ⊙O is 10cm, and the distances from the three points A, B, and C to the center of the circle are 8cm, 10cm, and 12cm respectively. Then the positional relationship between points A, B, C, and ⊙O is: point A is in _____; point B is in _ ____; Point C is at _____.
4. The radius of ⊙O is 6cm. When OP=6, point A is in ____; when OP _____, point P is inside the circle; when OP _____, point P is not outside the circle.
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"Positional Relationship between Points and Circles" Circle PPT Courseware:
"Positional Relationship between Points and Circles" Circle PPT Courseware Learning Objectives 1. Understand the positional relationship between points and circles; 2. Master the three-point circle theorem; 3. Master the definitions of the circumcircle and circumcenter of a triangle; 4. Understand the classification discussion and The idea of combining numbers and shapes; 5. Experience the joy of exploring mathematics...