Table of Contents
Circle
A circle is a simple closed shape. It is formed by a set of points, called the vertices, that are all the same distance from a fixed point, called the center. The distance from any point on the circle to the center is called the radius.
Circle Passing through 3 Points
A circle is a simple geometric shape that can be described by its center and radius. A circle can also be described by its points of intersection with other shapes. In this essay, we will explore the properties of a circle that passes through three points.
We will begin by constructing a coordinate plane. We will then mark three points on the coordinate plane. The points will be labeled P1, P2, and P3. We will then construct a circle that passes through P1, P2, and P3.
The center of the circle will be at the point (0, 0). The radius of the circle will be 6. The points P1, P2, and P3 will be on the circle.
We can see from the picture that the circle is symmetrical about the y-axis. The points P1, P2, and P3 are also symmetrical about the x-axis.
We can also see that the circle is tangent to the coordinate plane at P1 and P3. The line segment connecting P1 and P3 is called the diameter of the circle.
The equation of the circle is given by:
(x-0)2+(y-0)2=6
The Circle Passes through Collinear Points
If three points are collinear, that means they all lie on the same line. The Circle Passes through Collinear Points theorem states that if a circle passes through three collinear points, then the circle is tangent to the line that contains those points.
This theorem can be proven using a little bit of geometry. First, draw a circle and three points on it that are collinear. Next, draw a line through the points. The theorem states that the circle is tangent to the line that contains the points.
To prove that the theorem is true, we need to show that the circle is tangent to the line. We can do this by drawing a line that intersects the circle and the line that contains the points. If the line intersects the circle at two points, then the circle is not tangent to the line. However, if the line intersects the circle at one point, then the circle is tangent to the line.
In the diagram, the line intersects the circle at one point. Therefore, the circle is tangent to the line that contains the points.
The Circle Passes through Three Non-collinear Points.
This theorem states that if three non-collinear points are given, then the circle passing through those points will also be non-collinear.
Find the Equation of the Circle Passing through 3 Points
The equation of the circle passing through three points is:
(x-h)2+(y-k)2=r2
Creating a 3-Point Circle using a Compass and Straightedge
To create a 3-point circle, you will need a compass and a straightedge.
1. Draw a circle with the compass.
2. Draw a line from the center of the circle to the edge of the circle.
3. Draw a second line from the center of the circle to the other edge of the circle.
4. Connect the two lines to create your 3-point circle.
Some Important Key Points from Circles
The circle is a simple geometric shape that has many practical and mathematical applications.
A circle is defined as a set of points in a plane that are all the same distance from a given point, called the center.
The circumference of a circle is the distance around the edge of the circle.
The area of a circle is the amount of space inside the circle.
The radius of a circle is the distance from the center of the circle to its edge.
The diameter of a circle is the distance from one edge of the circle to the other edge, through the center.
Some Preparation Tips for Math Students Studying Circles
