The All-around shape: Circles
Question: What are circles and what are their important properties?
Section 1: Circles defined
Question: What is a circle?
Circle: A circle is a geometric shaped defined as the set of
all points in a plane equal distant from the central
point.
Section 2: Round and through
Question: How are the radius, diameter and circumference
related?
Radius: The radius is the distance from the center of a circle
to any point on the edge.
A circle showing the center point
(black dot), diameter (dashed
line), radius (double line) and a
secant (gray line)
Diameter: The diameter is the straight line distance from one point on the circle to the
point on the point on the opposite side.
Chord: The chord is a line between two points on a circle that are not on opposite sides
of a circle. A secant length is variable, but less than the diameter.
Circumference: The circumference is edge all of the way around the circle. It can also
refer to the length measured around the outside length of the circle.
Arc: An arc is a section of the circumference, the edge of the circle between any two
points on the circle
d = 2r
The diameter is twice the radius.
C = πd = 2πr The ratio between the circumference and the diameter is the special
number π = 3.14159…, and the ratio with the radius is 2π.
Section 3: Area
Question: What is the area of a circle and its components?
Area: The area of a circle is the measure of the entire two-dimensional space inside the
edge of the circle.
Section: A section is the area of a “pie slice” of the circle, formed by two radii from the
center to points on the edge of the circle and the arc between the two points.
Segments: A segment is the area bounded by the chord between two points on a circle
and the arc between them.
A = π r2
π.
The area of a circle is the square of the radius multiply by the special ratio