Analytic Foundations of Geometry

Robert S. Wilson

3. Equations of Circles

Definitions

A circle has a center and all of the points on the circle lie the same distance from the center.

The distance from a point on the circle to its center is called the radius of the circle.

The inside of a circle is the set of all points whose distance from the center is less than the radius.

The outside of a circle is the set of all points whose distance from the center is greater than the radius.

The distance from one side of a circle through the center to the other side is called the diameter of the circle.

A line is tangent to a circle if it meets the circle at exactly one point.

A line segment both of whose endpoints are both on a circle is called a chord of the circle.

A triangle is a figure determined by three points consisting of the three line segments joining the three points. The three points are called the three vertices, and the line segments between the vertices are called the sides of the triangle.

A right triangle is a triangle where two of the sides are perpendicular to each other.

In a right triangle, the side which is not perpendicular to one of the other sides is called the hypoteneuse.

A right angle is formed by two perpendicular lines.