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31 terms

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
Radius
'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
Perpendicular; radius
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
Arc Addition Postulate
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