Circles and the Three types of Symmetry

By Andrew Lee

Symmetry

• The correspondence in size, form and arrangement of parts on opposite sides of a plane, line, or point; arranged reciprocally or correspondingly.

What is a Circle?

• “A line forming a closed loop, every point on which is a fixed distance from a center point.”

• Has no edges.• Sum of angles inside is 360`• "The set of all points equidistant from the center". This

assumes that a line can be defined as an infinitely large set of points.

Properties• Center = A point inside the circle. All points on the circle are

equidistant (same distance) from the center point.• Radius = The radius is the distance from the center to any point on

the circle. It is half the diameter. • Diameter = The distance across the circle. The length of

any chord passing through the center. It is twice the radius. • Circumference = The circumference is the distance around the circle. • Area = Strictly speaking a circle is a line, and so has no area. What is

usually meant is the area of the region enclosed by the circle.• Chord = A line segment linking any two points on a circle.• Tangent = A line passing a circle and touching it at just one point. • Secant = A line that intersects a circle at two points.

A circle that has all three types of Symmetry

• Solution: - Use the equation x^2 + y^2 = r - x and y being a point on the circle and the r being the radius. note: when x or y is replaced by a (-x) or (-y) it will still remain the same, because (-x)^2 is equal to x^2. - it has to be symmetric with respect to the x-axis, y-axis and origin.