"Positional Relationship between Lines and Circles" Circle PPT Courseware 2

Description

"Positional Relationship between Lines and Circles" Circle PPT Courseware 2

Draw a circle and regard the edge of the ruler as a straight line. Fix the circle and translate the ruler.

What are the positional relationships between straight lines and circles?

There are three positional relationships:

When a straight line and a circle have a unique common point (that is, the straight line and the circle are tangent), the straight line is called the tangent line of the circle, and this unique common point is called the tangent point.

The definition of separation, tangency and intersection between a straight line and a circle.

The positional relationship between a straight line and a circle is defined by the number of common points between the straight line and the circle. That is, the straight line and the circle have no common points, only one common point, and two common points are called separation and tangency between the straight line and the circle respectively. ,intersect.

piece of cake:

Can we judge the positional relationship between a straight line and a circle based on basic concepts?

The number of common points between a straight line and a circle

New question:

Is there any other way to determine the positional relationship between a straight line and a circle?

Positional relationship between straight line and circle

d represents the distance from the circle center O to the straight line l, r represents the radius of ⊙O

When d>r, then the straight line l is separated from ⊙O

When d=r, then the straight line l is tangent to ⊙O

When d

fill in the blank:

1. It is known that the radius of ⊙O is 5cm and the distance between O and straight line a is 3cm. Then the positional relationship between ⊙O and straight line a is _____. The number of common points between straight lines a and ⊙O is ____.

2. It is known that the radius of ⊙O is 4cm, and the distance from O to straight line a is 4cm, then the positional relationship between ⊙O and straight line a is ___ _.

3. It is known that the radius of ⊙O is 6cm and the distance from O to straight line a is 7cm. Then the number of common points between straight line a and ⊙O is ____.

4. It is known that the diameter of ⊙O is 6cm, and the distance between O and straight line a is 4cm, then the positional relationship between ⊙O and straight line a is ___ _.

practise

1. Let the radius of ⊙O be 4, and the distance between point O and straight line a be d. If ⊙O and straight line a have at most one common point, then d is... ( )

A. d≤4 B. d<4 C. d≥4 D. d＝4

2. Suppose the radius of ⊙p is 4cm, and the distance from point A on the straight line l to the center of the circle is 4cm, then the positional relationship between the straight line l and ⊙O is... ( )

A. intersect B. tangent C. separate D. tangent or intersect

Knowledge sorting

1. There are three types of positional relationships between straight lines and circles: separation, tangency and intersection.

2. Methods to identify the positional relationship between straight lines and circles:

(1) One is to identify according to the definition:

Line L and ⊙o have no common points. Line L and ⊙o are separated from each other.

Line L and ⊙o have only one common point. Line L and ⊙o are tangent.

Line L and ⊙o have two common points. Line L and ⊙o intersect.

(2) The other is to identify based on the distance d between the center of the circle and the straight line and the radius r of the circle:

d>r The straight line L is separated from ⊙o;

d=r The straight line L is tangent to ⊙o;

d

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Update Time: 2024-09-23

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

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