"Positional Relationship between Lines and Circles" PPT download

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"Positional Relationship between Lines and Circles" PPT download

Part One: Classroom Activities

Activity 1. Review questions:

1. What are the positional relationships between points and circles?

2. How to determine the positional relationship between a point and a circle?

(1) When the distance from the point to the center of the circle is ____ radius, the point is outside the circle.

(2) When the distance from the point to the center of the circle is ____ radius, the point is on the circle.

(3) When the distance from the point to the center of the circle is ____ radius, the point is within the circle.

Activity 2

(1) As shown in the figure, when the sun rises, what are the positional relationships between the sun and the horizon? We regard the sun as a circle and the horizon as a straight line. From this, can you derive the positional relationship between the straight line and the circle?

(2) As shown in the figure, draw a straight line l on the paper. Think of the key ring as a circle. Move the key ring on the paper. You can find the number of common points between the key ring and the straight line l during the movement of the key ring. ?

(3) Can you demonstrate this process with real objects?

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?

PPT on the positional relationship between straight lines and circles, part 2: summary

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: A straight line and a circle have a unique common point, which 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.

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 and the circle are separated by d>r

2. The straight line is tangent to the circle d=r

3. The straight line intersects the circle d

PPT on the positional relationship between straight lines and circles, the third part: completing the drawing

Next, after we complete the drawing together, we will answer the questions:

(1) Draw an arbitrary ⊙O with radius r.

(2) Draw a radius OD of ⊙O arbitrarily.

(3) Draw a straight line l⊥OD through D.

The straight line l satisfies

First: passing through the outer end of the radius

Second: perpendicular to this radius

Theorem of tangent line determination: A straight line passing through the outer end of a radius and perpendicular to this radius is a tangent line to a circle.

Positional relationship between straight lines and circles PPT, Part 4: Application Migration

In △ABC, AB=10cm, BC=6cm, AC=8cm,

(1) If ⊙C is drawn with C as the center and 4 cm length as the radius, what is the positional relationship between ⊙C and AB?

(2) If AB is to be tangent to ⊙C, what should be the radius of ⊙C?

(3) If ⊙O is drawn with AC as the diameter, what is the positional relationship between ⊙O, AB, and BC?

Solution: Cross C to make CD⊥AB, and the vertical foot is D.

Because BC2+AC2=62+82=100, AB2=102=100,

So BC2+AC2=AB2, so △ABC is a right triangle. According to the equal area of ​​the triangles:

(1) If C is the center of the circle and 4cm is the radius, draw ⊙C. Because 4cm＜4.8cm, the positional relationship between ⊙C and AB is separated.

(2) If AB is to be tangent to ⊙C, the radius of ⊙C should be 4.8cm.

(3) If ⊙O is drawn with AC as the diameter, since BC⊥AC, ⊙O is tangent to BC; ⊙O intersects AB.

PPT on the positional relationship between straight lines and circles, part 5: practice in class

1. It is known that the radius of a circle is equal to 5 cm, and the distance from the center of the circle to the straight line l is: (1) 4 cm; (2) 5 cm; (3) 6 cm. How many common points do the straight line l and the circle have? State the positional relationship between the straight line l and the circle respectively.

2. It is known that the radius of the circle is equal to 10 cm, and the straight line l and the circle have only one common point. Find the distance from the center of the circle to the straight line l.

3. If the diameter of ⊙O is 10 cm, and the distance from the center of the circle O to the straight line AB is 10 cm, what is the positional relationship between ⊙O and the straight line AB?

4. Known: As shown in the figure, ∠AOB=30°, P is a point on OB, and OP=5 cm. What is the positional relationship between a circle with P as the center and R as the radius and the straight line OA? Why?

①R=2cm;

②R=2.5cm;

③R=4cm.

Keywords: Free download of mathematics PPT courseware for the second volume of the ninth grade of Hebei Education Edition, PPT download of the positional relationship between straight lines and circles, .PPT format;

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"Positional Relationship between Lines and Circles" PPT courseware download:

"Positional Relationship between Straight Lines and Circles" PPT Courseware Download Part One Content: Positional Relationships between Straight Lines and Circles: (1) There are two common points when a straight line intersects a circle; (2) There is only one common point when a straight line intersects a circle; (3) The straight line and the circle are separate and have no common points; Question:..

"Positional Relationship between Lines and Circles" PPT:

"Positional Relationship between Lines and Circles" PPT Part 1: Review Review What are the positional relationships between points and circles? The distance from the point to the center of the circle is d. The radius of ⊙O is r (1) dr point A is inside the circle (2) d=r point B is on the circle (3) dr point C is outside the circle. Three position relationships...

"Positional Relationship between Lines and Circles" PPT courseware 2:

"Positional Relationship between Straight Lines and Circles" PPT Courseware 2 Explore: When the straight line l in the picture meets what conditions is it a tangent to ⊙O? Method 1: The straight line and the circle have the only common point. Method 2: The distance from the straight line to the center of the circle is equal to the radius. Note: In the actual proof process, the first...

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Update Time: 2024-07-04

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