A. Definitions
1. A circle is defined by the equation:
(x-a)2 + (y-b)2 = r2
where r is the radius and (a,b) is the midpoint of the circle
2. The radius of a circle is the length from the edge of the circle to the midpoint.
3. The diameter of a circle is the length of a segment from one edge of the circle to the opposite edge of the circle in which the segment passes through the midpoint.
4. A chord is a segment that connects 2 sides of the circle but does not have to pass through the midpoint.
5. A tangent line is a line that connects with a circle in exactly one point and is perpendicular with the radius at that point.
B. Basic Memorizations
Area = 
Area
= 
Circumference
= 
or 
Diameter
= 
C. Examples
Ex [1] The diameter of a circle is equal to the circles area. The radius is ______.
a. If the diameter is equal to its area then we have: (d/2)2 = d. The only way this is possible is if the diameter is 4. Therefore the radius must be half this amount or 4.
b. The answer is 4.
Ex [2] The ratio of the circumference to the area of a circle with a radius of 5 is ________.
a. The
circumference of this circle is 
and the area is 
.
So the ratio is 
.
b. The answer is 2/5.