# Circles

### Terms

### Angle-Arc Theorem

In congruent circles, two central angles are congruent if and only if their intercepted arcs are congruent.### Angle-Chord Theorem

In congruent circles, two chords are congruent if and only if their associated central angles are congruent.### Arc

A segment of a circle. Different from the ark sought by Dr. Indiana Jones.### Arc-Chord Theorem

In congruent circles, two chords are congruent if and only if their associated arcs are congruent.### Arc Length

The distance a bug would crawl from one endpoint of the arc to the other, staying on the arc the whole time. The length of an arc with measure*θ*and radius

*r*is

### Arc Measure

The measure of an arc is equal to the measure of the central angle it subtends.### Central Angle

An angle whose vertex is the center of a circle. No relation to Central Park, which is a rectangle.### Chord

A line segment whose endpoints are both on a circle. Not a collection of musical notes.**Circle**

The set of all points in a plane that are exactly *r*units away from point

*O*, where

*r*is the radius and

*O*is the center. The basis for such artifacts as wheels, wedding rings, and many types of cookies. We write "⊙

*O*" to denote "the circle with center

*O*."

### Circumference

The arc length of a circle (note that a circle is an arc with measure 360°).### Diameter

A chord of a circle that contains the center of that circle. Or, you know, the length of such a chord.### Endpoint-Tangent Theorem

Any two segments that share an endpoint and are tangent to the same circle are congruent. Think of this as the Ice Cream Cone Theorem.### Exterior

The set of all points such that the distance from the center of the circle to that point is greater than the length of the radius. The wild, free, sunny open range outside the cold grip of ⊙*O*.

### Inscribed Angle

An angle whose vertex is on a circle and whose sides contain two chords of the same circle.### Inscribed Angle Theorem

For an inscribed angle ∠*ABC*containing points

*A*and

*C*, the measure of the arc

*AC*is twice the measure of ∠

*ABC*. Symbolically, m

*AC*= 2 × m∠

*ABC*.

### Interior

The set of all points such that the distance from the center of the circle to that point is less than the length of the radius. The territory enclosed by the grim, gray, chain-link-and-razor-wire fence ⊙*O*.

### Major Arc

An arc with measure greater than 180°. Major arcs aren't officers of the armed forces.### Minor Arc

An arc with measure less than 180°. Does not work in mines.### Perpendicular Tangent Theorem

A tangent line is always perpendicular to the circle's radius at the point of intersection.### Radius

A line segment with one endpoint at the center of a circle and the other endpoint on the circle itself. Alternatively, the length of such a segment. (The plural is*radii*, pronounced "raidy eye.")

### Secant

A line that intersects a circle at two points. Really, line, how intrusive can you get?### Semicircle

An arc with measure equal to 180°. Half a circle.### Tangent

A line that intersects a circle at exactly one point (the point of tangency). The word "tangent" literally means "touching." So a line tangent to a circle is "just touching" the circle.### Tangent Segment

A segment of a tangent line, one of whose endpoints is the point of tangency.Advertisement

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