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Authoritative PPT Summary
"Circle Through Three Points" PPT Courseware 2
think:
An archaeologist found a incomplete funerary tile in an ancient tomb (according to records, the original shape was round). As shown in the picture, can you help him restore it to its original shape?
Exploration 1
How many circles can you draw through a point in the plane?
Countless circles can be drawn through a point on the plane. The center of the circle is any point except point A, and the radius is the distance between this point and A.
Exploration 2
Draw a circle through two points A and B. How many circles can be drawn?
Countless circles can be drawn through two points A and B. The center of the circle is on the perpendicular bisector of AB, and the radius is the distance between this point and A or B.
Exploration 3
How many circles can be drawn through three points in the same plane?
Example: Given: three points A, B, C that are not on the same straight line,
Find the construction of circle O such that it passes through points A, B, and C.
Method: 1. Connect AB and draw the vertical bisector DE of line segment AB.
2. Connect BC, draw the perpendicular bisector FG of line segment BC, and intersect DE at point O.
3. Construct a circle with O as the center and OB as the radius.
Consolidate training
1. Judgment:
(1) Countless circles can be drawn through two points ( )
(2) A triangle whose vertices are all on a circle is called a circumscribed triangle of a circle ( )
(3) The distances from the circumcenter of the triangle to the three sides are all equal ( )
(4) The three vertices of a triangle are not necessarily cocircular ( )
(5) A triangle has only one circumcircle, and a circle has only one inscribed triangle ( )
2. Fill in the blanks:
As shown in the figure, △ ABC is the _____ triangle of circle O; circle O is the _____ circle of △ ABC.
3. As shown in the figure, there is a T-square, and CD is the perpendicular bisector of AB. How to use such a tool to find the center of a circular workpiece?
Class summary
After one point, you can make countless circles
Countless circles can be drawn through two points
Determine a circle passing through three points that are not on the same straight line
A circle cannot be drawn through three points on the same straight line
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"A Circle Through Three Points" PPT courseware:
"A Circle Through Three Points" PPT courseware 1. A circle is _________ at three points that are not at _______________. 2. A circle can be drawn through the three vertices of a triangle. This circle is called the ________ of the triangle. The center of the circumscribed circle is called the ________ of the triangle. 3. three..