Diameter the largest distance between any two points on the circle. This length is two of the radius
Chord a line segment between any two points on the circle. (Chord < Diameter)
Tangent a line that touches the circle at a single point
Secant a line that runs through two points on the circle.
Arc a part of the circles circumference.
Sector a part of the circle (an arc) with two side lengths equal to the radius.
Segment a part of the circle bounded by an arc and a chord.
(Coxeter, 1967)
Properties of circles have been discovered over time, but there is no real record as to when they were discovered. The area of a circle has been solved in many different ways. Three well known methods of discovering the area of a circle are Ahmes, Archimedes, and the formula used in schools today; 2pi*r^2. (Click on the two links above to go to applets that will help you further your knowledge of the methods Ahmes and Archimedes used to find the area of a circle.) (Eisenlohr,1877)
The equation of a circle is x ^2 + y^2 = r^2.
If CP = r, then using the distance formula;
r = the square root of [(x-0)^2 + (y-0)^2]
(x-0)^2 + (y-0)^2 = r2
x^2 +y^2 = r^2
If the center C is not on the origin, we can still use the distance formula to find the equation of the circle. (Kornilowicz, 2004)
r = the square root of [(x-p)^2 + (y-q)^2]
(x-p)^2 + (y-q)^2 = r^2