Top 10 things to know about circles
- A circle is the set of points in a plane that are
equidistant from a given point called the center.
- The distance from the center is called the radius,
and the point is called the center.
Twice the radius is known as the diameter, .
- The angle a circle subtends from its center is a full
angle, equal to or radians.
- The perimeter of a circle is called the circumference, and
is given by
- The area of a circle is given by .
- A central angle is an angle with endpoints and located
on a circle's circumference and vertex located at the circle's
- For an inscribed angle and central angle with the same
- A tangent to a circle at a point is perpendicular to the
- The circumcircle is a triangle's circumscribed circle, i.e.,
the unique circle that passes through each of the triangle's three
vertices. The center of the circumcircle is called the
circumcenter, and the circle's radius is called the
circumradius. A triangle's three perpendicular bisectors (i.e. the
line perpendicular to the side from the midpoint of the side)
meet at .
- The incircle is the inscribed circle of a triangle , i.e.,
the unique circle that is tangent to each of the triangle's three
sides. The center of the incircle is called the incenter, and the
radius of the circle is called the inradius. The incenter is the
point of concurrence of the triangle's angle bisectors.
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Steven R. Dunbar
Department of Mathematics and Statistics
University of Nebraska-Lincoln
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