Term

Definition
The set of points in a plane that lies at a positive fixed distance from some specific point. 


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Definition
The positive fixed distance from each point lying on the circle to the circle's center. 


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Definition of interior point 

Definition
For point P and circle O with radius r, if OP < r, then P is an _______ to circle O 


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Definition of exterior point 

Definition
For point P and circle O with radius r, if OP > r, then P is an _______ to circle O 


Term

Definition
For point P and Line L, the distance from P to L is the length from P to the foot of Q, where Q is perpendicular to L and drawn from P. 


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Definition of equidistant 

Definition
A point is __________ from two lines iff the distances from the point to each of the two lines are equal. 


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Definition: The set of points in a plane that lies at a positive fixed distance from some specific point. 

Definition


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Definition: The positive fixed distance from each point lying on the circle to the circle's center. 

Definition


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Definition: For point P and circle O with radius r, if OP < r, then P is an _______ to circle O 

Definition


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Definition: For point P and circle O with radius r, if OP > r, then P is an _______ to circle O 

Definition


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Definition: For point P and Line L, the distance from P to L is the length from P to the foot of Q, where Q is perpendicular to L and drawn from P. 

Definition


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Definition: A point is __________ from two lines iff the distances from the point to each of the two lines are equal. 

Definition


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Definition


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Definition


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Definition


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Illustration of Central angle 

Definition


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Illustration of Inscribed angle 

Definition


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Definition


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Illustration of Subtended arc of an angle 

Definition


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Illustration of Angle inscribed in a semicricle 

Definition


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Definition


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Definition


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Definition


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Definition


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Definition


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Definition


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Definition
Subtended arc of an angle 


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Definition
Angle inscribed in a semicricle 


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Definition
The intersection of a circle with the interior points of a central angle 


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Definition: The intersection of a circle with the interior points of a central angle 

Definition


Term

Definition
Intersection of a circle and the closed half plane lying on one side of a diameter of the circle 


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Definition: Intersection of a circle and the closed half plane lying on one side of a diameter of the circle 

Definition


Term

Definition
Intersection of a circle with the exterior points of a central angle 


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Definition: Intersection of a circle with the exterior points of a central angle 

Definition


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Definition of Measure of an arc 

Definition
A real number number existing in (0,360) corresponding to the measure of a central angle of a circle 


Term
Definition of measure for a minor arc 

Definition
the measure of the arc is the measure of the central angle 


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Definition of measure for a major arc 

Definition
the measure of the arc is 360 minus the measure of the central angle 


Term
If the end points of an arc lie on a diameter... 

Definition
...then the measure of the arc is 180 


Term

Definition
A line that meets a circle in two distinct points 


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A line that meets a circle in two distinct points 

Definition


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Definition
A line that meets a circle at only one point 


Term
If C is a chord to circle O, and L is the perpendicular bisector of D... 

Definition
...Then L passes through point O. 


Term
If a line does not pass through the center of a circle... 

Definition
...Then the line is not the perpendicular bisector to any chord of the circle 


Term
If a line passes through the center of a circle, and is perpendicular to a chord of that circle... 

Definition
...Then the line is the perpendicular bisector to the chord 


Term
An angle is said to _______ an arc iff the intersection between the arc and the angle's defining rays is the end points of the arc. 

Definition


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A chord is said to _______ an arc iff the intersection between the arc and the chord is the end points of the arc. 

Definition


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If two chords have the same measure, then they are _________ (definition). 

Definition


Term
if two central angles are congruent... 

Definition
...then their subtended chords are congruent 


Term
if two chords are congruent... 

Definition
...then their subtending central angles are congruent 


Term
if two chords are equidistant from the center of a circle... 

Definition
...then the chords are congruent 


Term
if two chords are congruent... 

Definition
...then the chords are equidistant from the center of the circle 


Term
(THM 3.8.1) If two arcs of a circle have one and only one point in common... 

Definition
...then the union of those two arcs is also a an arc 


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(THM 3.8.1) If an arc can be shown to be a union of two arcs... 

Definition
...then the measure of the union arc is the sum of the measures of the arcs in the union 


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(THM 3.8.2) A line is tangent to a circle if and only if... 

Definition
...the line is perpendicular to the circle's radius at the point of contact 


Term
(THM 3.8.2) If a line is not perpendicular to a circle's radius at a point of contact... 

Definition
...then the line is not tangent to the circle 


Term
(LEMMA 3.8.A) Given a ray AB and any point O, define d(x) for nonnegative real x as the distance from O to P on AB, where x is the coordinate of P when A has coordinate 0. Then... 

Definition


Term
(THM 3.8.3) If a line L passes through an interior point A of a circle... 

Definition
...then the line is a secant of the circle, and thus intersects the circle at exactly two points 

