# Geometry Chapter 12

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### Circle; center

The set of all points in a plane that are at a given distance from a given point in the plane; named for its _____

### Concentric

Circles iff they lie in the same plane and have the same center

'A"': For a circle, the segment that connects the center of it to any point on it; 'the': The length of one of the aforementioned line segments

### Corollary to the definition of a circle

All radii of a circle are equal

### Chord

For a circle, the line segment connecting two points of the circle

### Diameter

'A': A chord that connects the center of the circle; 'the': the length of one of the aforementioned line segments

### Line; perpendicular; bisects

If a ____ through the center of a circle is ____________ to a chord, it also _______ the chord

### Line; bisects; diameter; perpendicular

If a ____ through the center of a circle _____ a chord that is not a _________, it is also ____________ to the chord

### Perpendicular bisector

The ___________ _________ of a chord of a circle contains the ______ of the circle

### Tangent; one

For a circle, the line in the plane that intersects the circle in exactly ___ point

### Tangent; perpendicular

If a line is _______ to a circle, it is ___________ to the radius drawn to the point of contact

If a line is ____________ to a ______ at its outer endpoint, it is tangent to the circle

### Semicircle

Half of a circle; is 180°

### Minor arc

The part of a circle less than 180°

### Major arc

The part of a circle bigger than 180°

### Central angle; vertex

For a circle, an angle whose ______ is the center

### Reflex angle

An angle whose measure is greater than 180°

### Measure of an arc

This is equal to the measure of its central angle

If point C is on arc AB, then mAC + mCB = mACB

### Equal; arcs

In a circle, _____ chords have equal _____

### Arcs; equal

In a circle, equal _____ have _____ chords

### Inscribed angle

For a circle, an angle whose vertex is on the circle, with each of the angle's sides intersecting the circle in another point

### Inscribed; half

An _______ angle is equal in measure to ____ its intercepted arc

### Arc; equal

Inscribed angles that intercept the same ____ are _____

### Semicircle; right

An angle inscribed in a _________ is a _____ angle

### Secant

A line that intersects a circle in two points

### Secant angle

An angle whose sides are contained in two secants of a circle so that each side intersects the circle in at least one point other than the angle's vertex

### Secant; half; arcs

A ______ angle whose vertex is inside a circle is equal in measure to ____ the sum of the ____ intercepted by it and its vertical angle

### Outside; larger; smaller

A secant angle whose vertex is ______ a circle is equal in measure to half the difference of its ______ and ______ intercepted arcs

### Tangent Segments Theorem

The tangent segments to a circle from an external point are equal

### Intersecting Chords Theorem

If two chords intersect in a circle, the ______ of the lengths of one chord is equal to the product of the lengths of the other chord

Example: