"Positional Relationship between Lines and Circles" Circle PPT Courseware 3

Description

"Positional Relationship between Lines and Circles" Circle PPT Courseware 3

learning target

1. Master the three positional relationships between straight lines and circles;

2. Master the properties and determination theorem of tangent lines;

3. Understand the ideas of classification discussion and combination of numbers and shapes;

4. Experience the fun of exploring mathematics.

Draw a circle on the paper, think of the ruler as a straight line, and move the ruler.

Can you find the change in the number of common points between straight lines and circles? How many common points are there at least? How many are there at most?

There are ____ methods to determine the positional relationship between a straight line and a circle:

(1) According to the definition, it is judged by the number of __________;

(2) According to the nature, it is judged by the relationship of __________.

basic training

1. It is known that the diameter of the circle is 13cm, and the distance between the straight line and the center of the circle is d:

1) If d=4.5cm, then the straight line and the circle ______, and the straight line and the circle have ____ common points.

2) If d=6.5cm, then the straight line and the circle ______, and the straight line and the circle have ____ common points.

3) If d= 8 cm, then the straight line and the circle ______, and the straight line and the circle have ____ common points.

2. It is known that the radius of ⊙O is 5cm, the distance between the center O and the straight line AB is d, fill in the range of d according to the conditions:

1) If AB and ⊙O are separated, then ______;

2) If AB and ⊙O are tangent, then ______;

3) If AB and ⊙O intersect, then ______;.

Question exploration

Please pick any point A on ⊙O and connect OA. Draw a straight line l⊥OA through point A. Think about the questions:

1. What is the quantitative relationship between the distance from the center O of the circle to the straight line l and the radius of the circle?

2. What is the relationship between the two locations? Why?

3.What did you discover from this?

There are three ways to prove that a straight line is tangent to a circle:

1. Definition: A straight line that has one and only one common point with a circle is a tangent to a circle.

2. Quantity method (d=r): The straight line whose distance from the center of the circle is equal to the radius is the tangent line of the circle.

If the common point of the straight line and the circle is not specified, draw a perpendicular segment of the straight line through the center of the circle, and then explain that the length of this line segment is equal to the radius of the circle.

3. Determination theorem: A straight line passing through the outer end of the radius and perpendicular to the radius is a tangent to the circle.

If a common point between the straight line and the circle is specified, connecting this point to the center of the circle means that the straight line is perpendicular to the radius passing through this point.

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For more information about the "Positional Relationship between Circles, Straight Lines and Circles" PPT courseware, please click the "Positional Relationship between Circles, Straight Lines and Circles" ppt tag.

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Update Time: 2024-11-24

This template belongs to Mathematics courseware People's Education Press Ninth Grade Mathematics Volume 1 industry PPT template

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