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Authoritative PPT Summary
"Determining the Conditions of a Circle" Circle PPT Courseware 4
learning target
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 concepts such as the circumcircle of a triangle and the circumcenter of a triangle.
3. Experience the exploration process of determining a circle from three points that are not on the same straight line, and cultivate your exploration ability.
Draw a circle through the known points A and B. Countless circles can be drawn.
How are you going to make a circle (determine the center and radius)?
What are the characteristics of the distribution of the center of the circle? What is its relationship with the line segment AB?
in conclusion:
1. The center of the circle passing through two points A and B is on the perpendicular bisector of line segment AB.
2. Take any point on the perpendicular bisector of line segment AB as the center of the circle, and the distance from this point to A or B as the radius to draw a circle.
【example】
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. Construct a circle with O as the center and OB as the radius. ⊙O is the circle you want to construct.
【Tracking Training】
Now do you know how to restore a broken disk as shown in the picture?
method:
1. Pick three points A, B, 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 the length of OC as the radius.
⊙O is what you want.
Definition: The circle passing through each vertex of a 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 in class
1. (Hebei High School Entrance Examination) As shown in the figure, in a 5×5 square grid, an arc passes through three points A, B, and C. Then the center of the circle where this arc is located is ( )
A. Point P B. Click Q C. Click R D. Point M
2. (Urumqi High School Entrance Examination) As shown in the figure, in the plane rectangular coordinate system, the coordinates of points A, B, and C are (1, 4), (5, 4), (1, -2) respectively, then △ABC The coordinates of the center of the circumscribed circle are ( )
A.(2,3) B.(3,2)
C.(1,3) D.(3,1)
3. (Jiangxi High School Entrance Examination) As shown in the figure, the arc with point P as the center intersects with the x-axis at two points A and B. The coordinates of point P are (4, 2), and the coordinates of point A are (2, 0) , then the coordinates of point B______.
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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 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 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..