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"Determining the Conditions of a Circle" Circle PPT Courseware 5
Knowledge review:
1. The practice and properties of vertical 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?
Explore one
Can a circle be determined through a known point A?
Exploration 2
Can a circle be made through two known points A and B?
Countless circles can be drawn 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?
draw a picture
Known: three points A, B, C that are not on the same straight line
Find the solution: ⊙O makes it pass through points A, B, and 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. A circle cannot be drawn 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.
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 Conditional Circle of a Circle", please click the "Determining the Conditional Circle of a Circle" ppt circle ppt tag.
"Determining the Conditions of a Circle" PPT courseware:
"Conditions for Determining a Circle" PPT courseware learning objectives 1. Knowledge and skills: ① Understand how three points that are not on the same straight line determine a circle; ② Master the method of making a circle with three points that are not on the same straight line; ③ Understand the principles of triangles Concepts such as circumcircle and circumcenter of triangle...
"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..