"Determining the Conditions of a Circle" PPT courseware

Description

"Determining the Conditions of a Circle" PPT courseware

learning target

1.Knowledge and skills:

① Understand that three points that are not on the same straight line determine a circle;

② Mastered the method of making a circle from three points that are not on the same straight line;

③Understand concepts such as the circumcircle of a triangle and the circumcenter of a triangle, and improve the ability to apply mathematical knowledge to solve practical problems.

2. Process and methods: Experience the exploration process of determining a circle from three points that are not on the same straight line, and experience induction, analogy and mathematical thinking methods from special to general.

3. Emotional attitudes and values: In exploratory activities, students are encouraged to develop the learning quality of being brave enough to explore, understand strategies for solving problems, and learn to think mathematically.

Knowledge in life

An archaeologist discovered a circular porcelain fragment while excavating the Mawangdui Han Tomb in Changsha. Can you help the archaeologist draw the complete circle where the fragment is located to facilitate in-depth research?

think about it

What is the key to determine a circle?

Determine the center and radius of a circle

Knowledge review

1. How many straight lines can be drawn through a point?

2. At what point can a straight line be determined?

At what point can a circle be determined?

Exploration 1 Can a circle be determined through a known point A?

Exploration 2 Can a circle be determined through two known points A and B?

On what straight line is the center of a circle drawn through two known points A and B?

Their centers are all on the mid-perpendicular to line segment AB.

Exploration 3 Can a circle be determined through three known points A, B, and C?

Assume that ⊙O exists through three points A, B, and C

(1) The distance from the center O to the three points A, B, and C is _________.

(2) Connect AB, AC, ________

Point O should be on _________ of AB;

At the same time, point O should also be on _________ of AC.

(3) The center O of the circle should be the intersection point of the perpendicular bisectors of AB and BD

Known: three points A, B, C that are not on the same straight line

Find: ⊙O makes it pass through points A, B, C

Method: 1. Connect AB and draw the perpendicular bisector MN of line segment AB;

2. Connect AC, draw the perpendicular bisector EF of line segment AC, and intersect MN at point O;

3. Draw a circle with O as the center and OB as the radius. So ⊙O is the circle you want to make.

Now you know how to restore a broken disk as shown in the picture?

Method: 1. Pick three points A, B, and C on the arc.

2. Draw the perpendicular bisectors of line segments AB and BC, and their intersection point O is the center of the circle.

3. Construct a circle with point O as the center and length OC as the radius.

⊙O is what you want.

definition

The circle passing through each vertex of the triangle is called the circumcircle of the triangle. The center of the circumscribed circle is called the circumcenter of the triangle. This triangle is called the inscribed triangle of the circle.

As shown in the figure: ⊙O is the circumcircle of △ABC, △ABC is the inscribed triangle of ⊙O, and point O is the circumcenter of △ABC.

The circumcenter is the intersection point of the perpendicular bisectors of the three sides of △ABC, which is equidistant from the three vertices of the triangle.

practice

1.Which of the following propositions is incorrect?

A. There are countless circles passing through one point. B. There are countless circles passing through two points.

C. A chord is a part of a circle. D. It cannot pass through three points on the same straight line.

2. The properties of the circumcenter of a triangle are:

A. The distance to the three sides is equal. B. The distance to the three vertices is equal.

C. The circumcenter is outside the triangle. D. The circumcenter is inside the triangle.

3.The intersection point of the height of the base of an isosceles triangle and the vertical bisector of one waist is

A. Center of gravity, B. Vertical center, C, Circumcenter, D. Unable to determine.

judge:

1. A circle can be drawn through three points. ( )

2. The circumcenter of a triangle is the intersection point of the perpendicular bisectors on both sides of the triangle. ( )

3. The distances from the circumcenter of the triangle to the three sides are equal. ( )

4. The circumcenter of an isosceles triangle must be within this triangle. ( )

Talk about harvest:

(1) Only when the center and radius of the circle are determined can the position and size of the circle be uniquely determined.

(2) Countless circles can be drawn through a known point!

(3) Countless circles can be drawn through two known points A and B! The centers of these circles are on the perpendicular bisector of line segment AB.

(4) Three points that are not on the same straight line determine a circle.

(5) The concept of circumscribed circle and circumcenter.

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For more information about the PPT courseware "Determining the Conditions of a Circle", please click the "Determining the Conditions of a Circle" ppt tab.

"Determining the Conditions of a Circle" Circle PPT Courseware 5:

"Determining the Conditions of a Circle" Circle PPT Courseware 5 Knowledge review: 1. The method and properties of perpendicular bisectors of line segments 2. How many straight lines can be drawn through a point? 3. At what point can a straight line be determined? Exploration 1 Can a circle be determined through a known point A? Exploration 2 Passed...

"Determining the Conditions of a Circle" Circle PPT Courseware 4:

"Conditions for Determining a Circle" Circle PPT Courseware 4 Learning Objectives 1. Understand how to determine a circle from three points that are not on the same straight line, and how to draw a circle through three points that are not on the same straight line. 2. Understand the circumcircle of a triangle, Concepts such as the circumcenter of a triangle. 3. Experiences are not the same..

"Determining the Conditions of a Circle" Circle PPT Courseware 3:

"Conditions for Determining a Circle" Circle PPT Courseware 3 Knowledge Review 1. The circumferential angle subtended by the diameter is a right angle; 2. The chord subtended by the circumferential angle of 90 is the diameter. 3. The four vertices of quadrilateral ABCD are all on ⊙O. Such a quadrilateral is called a circle inscribed quadrilateral; this circle is called a quadrilateral..

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Update Time: 2024-11-19

This template belongs to Mathematics courseware Qingdao Edition Ninth Grade Mathematics Volume 1 industry PPT template

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