Circle geometry is the study of the properties and relationships of circles. A circle is defined as the set of all points in a plane that are equidistant from a fixed point called the center. Key elements include the radius, which is the distance from the center to any point on the circle, and the diameter, which is twice the radius and passes through the center. Important concepts in circle geometry include circumference, the distance around the circle, and area, the space enclosed by the circle. The relationships between angles, chords, tangents, and arcs are also significant, helping to understand how circles interact with other geometric shapes.