"Positional Relationship between Lines and Circles" PPT courseware

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"Positional Relationship between Lines and Circles" PPT courseware

Review and review

Question 1: What are the positional relationships between points and circles?

d represents the distance from the point to the center of the circle, r represents the radius of the circle

Point outside the circle d>r

Point on the circle d=r

Point is inside the circle d

Combining Numbers and Shapes: Positional Relationships Quantitative Relationships

Use your brain to think

(1) How does the number of common points of straight lines and circles change? How many are the minimum number of public points? How many are there at most?

(2) Through the research just now, how many types do you think the positional relationship between straight lines and circles can be divided into?

Let’s summarize it together:

1. The positional relationship between straight lines and circles (graphical features----distinguished by the number of common points)

Features: A straight line and a circle have two common points, which are called intersections of the straight line and the circle. The straight line at this time is called the secant of the circle.

Features: The only common point between a straight line and a circle is called tangent between the straight line and the circle. The straight line at this time is called a tangent line, and the only common point is called a tangent point.

Features: A straight line and a circle have no common points, which is called a straight line and a circle that are separated from each other.

A little experience

We can judge the positional relationship between a straight line and a circle based on the number of common points between the straight line and the circle.

Discuss: Following the method of determining the positional relationship between a point and a circle, do you have any other methods to determine the positional relationship between a straight line and a circle? Can it be judged based on the quantitative relationship between the distance from the center of the circle to the straight line and the radius of the circle?

Observation and discussion: When a straight line is separated from, tangent to, or intersected with a circle, what is the relationship between the distance d from the center of the circle and the straight line and the radius r?

1. The straight line is separated from the circle

2. The straight line is tangent to the circle

3. The intersection of a straight line and a circle

summary:

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 common points between the straight line and the circle;

(2) According to the properties, it is judged by the relationship between the distance d from the center of the circle to the straight line and the radius r.

In practical applications, the second method is often used to determine.

Small scale chopper

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= 8cm, 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 d > 5cm;

2) If AB and ⊙O are tangent, then d = 5cm;

3) If AB and ⊙O intersect, then 0cm≤d<5cm.

self-examination

1. It is known that the diameter of the circle is 13cm. If the distance between the straight line and the center of the circle is the following value, how many common points do the straight line and the circle have? Why?

(1) 6cm

A 0 pieces; B 1 piece; C 2 pieces;

(2) 6.5cm

A 0 pieces; B 1 piece; C 2 pieces;

(3) 7cm

A 0 pieces; B 1 piece; C 2 pieces;

2. As shown in the figure, it is known that ∠BAC=30 degrees, M is a point on AC, and AM=5cm. What is the positional relationship between a circle with M as the center and r as the radius and the straight line AB? Why?

(1) r=2cm

(2) r=4cm

(3) r=2.5cm

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Update Time: 2024-10-03

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