"Why are wheels made round?" Circle PPT courseware 4

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"Why are wheels made round?" Circle PPT courseware 4

Why are round wheels stable?

(1) As shown in the figure, A and B represent two points on the edge of the wheel, and O represents the axis of the wheel. What is the relationship between the distance between A and O and the distance between B and O?

(2) C represents any point on the edge of the wheel. If the wheel can roll smoothly, what relationship should be satisfied between the distance between C and O and the distance between A and O?

The distance from any two points on the wheel edge to the axis center is equal, and the distance from any point to the axis center is a fixed value.

The distance from a point on a circle to the center of the circle is a constant value

Definition of a circle: A figure composed of all points on a plane whose distance from a fixed point is equal to a fixed length is called a circle.

The fixed point is called the center of the circle

The fixed length is called the length of the radius (referred to as the radius)

A circle with point o as the center is denoted as ⊙o and pronounced as "circle o"

Note: 1. From the definition of a circle, we can know that a circle refers to the circumference rather than the surface.

2. The elements that determine a circle are: center and radius.

explore

What is the relationship between the distances from points A, B, C, D, and E to the center O and the radius of ⊙O?

The distance from points A and C to the center of the circle is less than the radius

The distance from point B to the center of the circle is equal to the radius

The distance from points D and E to the center of the circle is greater than the radius

Consolidate new knowledge and apply new knowledge

practice

1. Given that the area of ​​⊙O is 25π, determine the positional relationship between point P and ⊙O.

(1) If PO=5.5, then point P is at ___;

(2) If PO=4, then point P is at ___;

(3) If PO=___, then point P is on the circle.

2. In Rt△ABC, ∠C=90°, AC=3, BC=4, and D is the midpoint of AB

(1) Taking C as the center of the circle and the length AC as the radius, then the positional relationship between point D and circle C.

(2) Taking C as the center of the circle and BC as the radius, then the positional relationship between point D and circle C.

draw a picture

Given that AB=3cm, draw a figure that meets the following requirements:

(1) The graph composed of all points whose distance to point A is equal to 2cm.

(2) The graph composed of all points whose distance to point B is equal to 2cm.

(3) The graph composed of all points whose distance to points A and B is equal to 2cm.

(4) The graph composed of all points whose distance to point A and point B is less than 2cm.

Variations

Assume AB=4cm, draw a figure that meets the following requirements

1. The set of all points whose distance from point A is equal to 3cm and the distance from point B is equal to 2cm.

2. The set of all points whose distance from point A is less than 3cm and whose distance from point B is less than 2cm.

Known: As shown in the figure, the diagonals AC and BD of the rectangle ABCD intersect at point 0. Are its four vertices A, B, C, and D on a circle with point 0 as the center? Why?

Refined analysis: To prove that several points are on the same circle, you only need to prove that the distances from these points to a certain point are all away from each other. The key is to find this "fixed point"

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"Why are wheels made round?" Circle PPT courseware 3:

"Why Wheels Are Made Round" Circle PPT Courseware 3 Learning Objectives 1. Experience the process of forming the concept of a circle, and experience the process of exploring the positional relationship between points and circles. 2. Understand the concept of a circle and the positional relationship between points and circles. Why are round wheels stable? On the edge of the wheel...

"Why are wheels made round?" Circle PPT courseware 2:

"Why are wheels made round" Circle PPT Courseware 2 Learning Objective 1. Experience and perceive why wheels are made round; 2. Know the definition and representation of a circle; As shown in the figure, A and B represent two points on the edge of the wheel , point O represents the axis of the wheel, the distance between A and O..

"Why are wheels made round?" Circle PPT courseware:

"Why are wheels made round?" Circle PPT courseware Why are round wheels stable? (1) As shown in the figure, A and B represent the two points on the edge of the wheel, O represents the axis of the wheel, and the distance between A and O is the same as B , What is the relationship between the distance between O? (2)C means on the edge of the wheel..

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Update Time: 2024-11-06

This template belongs to Mathematics courseware Beijing Normal University Ninth Grade Mathematics Volume 2 industry PPT template

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