Definition:Circle

As defined by Euclid:

"A circle is a plane figure contained by one line such that all the straight lines falling upon it from one point among those lying within the figure are equal to one another."

Center
As defined by Euclid:

"And the point is called the center of the circle."

(Note: UK English spells this "centre".)

Circumference
The circumference of a circle is the line that forms its boundary.

Diameter
As defined by Euclid:

"A diameter of the circle is any straight line drawn through the center and terminated in both directions by the circumference of the circle, and such a straight line also bisects the circle."

Semicircle
As defined by Euclid:

"A semicircle is the figure contained by the diameter and the circumference cut off by it. And the center of the semicircle is the same as that of the circle.

Radius
A radius (plural "radii", pronounced "ray-dee-i") of a circle is a straight line segment whose endpoints are the center and the circumference of the circle.

Equality
As defined by Euclid:

"Equal circles are those the diameters of which are equal, or the radii of which are equal."