"Positional Relationship between Lines and Circles" PPT

"Positional Relationship between Lines and Circles" PPT

Part One: Review and Review

What are the positional relationships between points and circles?

The distance from the point to the center of the circle is d

⊙O radius is r

(1) d

(2) d=r←→Point B is on the circle

(3) d>r←→Point C is outside the circle

three positional relationships

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

Observation and exploration one

You found that this natural phenomenon reflects the number of common points of straight lines and circles in _______ situations.

Research activity two

Ask students to draw a circle in their exercise books. Think of the edge of the ruler as a straight line and translate the ruler. How many common points do the straight line and the circle have?

A straight line and a circle have two common points. At this time, we say that this straight line intersects the circle. This straight line is called the secant of the circle.

There is only one common point between a straight line and a circle. At this time, we say that this straight line is tangent to the circle. This straight line is called the tangent line of the circle, and this point is called the tangent point.

A straight line and a circle have no common points. In this case, we say that the straight line is separated from the circle.

The positional relationship between a straight line and a circle PPT, the third part: the position of a straight line and a circle

1. Positional relationship between straight lines and circles (number of common points)

1. There are three positional relationships between straight lines and circles (from the number of common points between straight lines and circles)

2. Represent graphically as follows:

There are two common points

There is a common point

no common points

2. Quantification of the positional relationship between straight lines and circles

Can you determine the positional relationship between the straight line and the circle based on the size relationship between d and r?

d: The distance between the center O of the circle and the straight line is d → draw the perpendicular segment of the straight line through the center of the circle

(1) The straight line and the circle intersect ←→d

(2) The straight line and the circle are tangent ←→d=r;

(3) The straight line and the circle are separated ←→d>r;

PPT on the positional relationship between straight lines and circles, part 4: Inspection in class

1. It is known that the radius of ⊙O is 6cm, the distance between the center of the circle 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 > 6cm;

2) If AB and ⊙O are tangent, then d = 6cm;

3) If AB and ⊙O intersect, then 0cm≤d < 6cm.

2. If a straight line and a circle have two intersection points, then the straight line and the circle ________;

If a straight line and a circle have an intersection point, then the straight line and the circle ________;

If the straight line and the circle have any intersection point, then the straight line and the circle ________;

PPT on the positional relationship between straight lines and circles, part five: flexible application

1. As shown in the figure: ∠AOB = 30°M is a point on OB, and OM =5 cm. What is the relationship between the circle with M as the center and r as the radius and the straight line OA? Why?

(1) r = 2 cm; (2) r = 4 cm; (3) r = 2.5 cm.

2. In Rt△ABC, ∠C=90°, AC=3cm, BC=4cm, the circle with C as the center and r as the radius and AB

What is the positional relationship? Why?

(1)r=2cm; (2)r=2.4cm (3)r=3cm.

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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 download:

"Positional Relationship between Lines and Circles" PPT Download Part One: Classroom Activities Activity 1. Review questions: 1. How many positional relationships are there 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. ..

"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...