"Positional Relationship between Straight Lines and Circles" Circle PPT Courseware 4

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"Positional Relationship between Straight Lines and Circles" Circle PPT Courseware 4

review review

What are the positional relationships between points and circles?

The distance from the point to the center of the circle is d, and the radius of the circle is r, then:

The point is outside the circle --- d>r;

Point on the circle --- d=r;

The point is inside the circle --- d

Combination of numbers and shapes: positional relationship---quantitative relationship

Explore new knowledge

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

(1) A straight line and a circle have two common points, which are called intersections of the straight line and the circle. This straight line is called the secant of the circle. These two common points are called intersection points.

(2) There is only one common point between a straight line and a circle, which is called the tangent point between the straight line and the circle. This straight line is called the tangent line of the circle, and this common point is called the tangent point.

(3) When a straight line and a circle have no common points, it is said that the straight line and the circle are separated.

Memories of relevant knowledge points

1. The length of the perpendicular segment from a point outside the straight line to the straight line is called the distance from the point to the straight line.

2. Among the line segments connecting a point outside the straight line and all the points on the straight line, which is the shortest perpendicular segment?

Summarize:

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, judged by the relationship of ______________.

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= 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 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 ______;

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

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

Example: In Rt△ABC, ∠C=90°, AC=3cm, BC=4cm, what is the positional relationship between the circle with C as the center and r as the radius and AB? Why?

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

Analysis: To understand the positional relationship between AB and ⊙C, you only need to know the relationship between the distance d and r from the center C to AB. Given r, we only need to find the distance d from C to AB.

Summary:

There are two ways 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.

self-examination

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) 4.5cm A 0 pieces; B 1 piece; C 2 pieces;

(2) 6.5cm A 0 pieces; B 1 piece; C 2 pieces;

(3) 8cm A 0 pieces; B 1 piece; C 2 pieces;

Expand and extend

It is known that the diameter of ⊙A is 6, and the coordinates of point A are (-3, -4), then the positional relationship between the x-axis and ⊙A is _____, and the positional relationship between the y-axis and ⊙A is _____.

Variation training

If ⊙A is to be tangent to the x-axis, how many units should ⊙A move upward? What if ⊙A wants to intersect the x-axis?

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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: 2024-11-17

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