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Circumference
The curved boundary (perimeter) of a circle.
Center
The point inside a circle that is the same distance from every point on the circumference.
Radius
A line segment from the center of a circle to a point on the circumference.
Diameter
A chord that passes through the center of the circle, its length is twice the radius.
Chord
A line segment joining two points on the circumference of a circle.
Arc
A part of the circumference of a circle between two points.
Segment
The region bounded by a chord and the arc between the chord’s endpoints.
Secant (in the circle)
A line that intersects a circle at two points.
Tangent (to a circle )
A straight line that touches the circle's circumference at exactly one point, called the point of tangency, without crossing into the interior
A tangent to a circle touches the circle at exactly one point (the point of contact).
A key property links tangents to the circle's center:
Tangent–radius theorem: If a line is tangent to a circle at point $T$ and $OT$ is the radius to the point of contact, then $$OT \perp \text{tangent at }T$$
In other words, the tangent is perpendicular to the radius drawn to the contact point.
Many circle problems involve angles subtended by the same chord or arc.
Angle subtended
An angle formed when two lines from a point meet two points on a circle. For example, chord $AC$ subtends an angle at the center $\angle AOC$ and an angle at the circumference $\angle ABC$.
Central angle theorem: For points $A,B,C$ on a circle with center $O$ (and with $B$ on the same side of chord $AC$ as the arc being used), $$\angle AOC = 2\angle ABC$$
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