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| The set of points in a plane that lies at a positive fixed distance from some specific point. |
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| The positive fixed distance from each point lying on the circle to the circle's center. |
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| Definition of interior point |
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| 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 |
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| For point P and circle O with radius r, if OP > r, then P is an _______ to circle O |
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| 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 |
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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. |
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| Definition: The set of points in a plane that lies at a positive fixed distance from some specific point. |
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Definition
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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
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| 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
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| 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: 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: A point is __________ from two lines iff the distances from the point to each of the two lines are equal. |
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| Illustration of Central angle |
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| Illustration of Inscribed angle |
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| Illustration of Subtended arc of an angle |
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| Illustration of Angle inscribed in a semicricle |
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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 |
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Definition
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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 |
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Definition
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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 |
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Definition
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| Definition of Measure of an arc |
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Definition
| A real number number existing in (0,360) corresponding to the measure of a central angle of a circle |
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| Definition of measure for a minor arc |
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Definition
| the measure of the arc is the measure of the central angle |
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| Definition of measure for a major arc |
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Definition
| the measure of the arc is 360 minus the measure of the central angle |
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| If the end points of an arc lie on a diameter... |
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Definition
| ...then the measure of the arc is 180 |
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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 |
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Definition
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Definition
| A line that meets a circle at only one point |
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| If C is a chord to circle O, and L is the perpendicular bisector of D... |
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Definition
| ...Then L passes through point O. |
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| If a line does not pass through the center of a circle... |
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Definition
| ...Then the line is not the perpendicular bisector to any chord of the circle |
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| If a line passes through the center of a circle, and is perpendicular to a chord of that circle... |
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Definition
| ...Then the line is the perpendicular bisector to the chord |
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| 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. |
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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. |
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Definition
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| If two chords have the same measure, then they are _________ (definition). |
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Definition
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| if two central angles are congruent... |
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Definition
| ...then their subtended chords are congruent |
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| if two chords are congruent... |
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Definition
| ...then their subtending central angles are congruent |
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| if two chords are equidistant from the center of a circle... |
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Definition
| ...then the chords are congruent |
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| if two chords are congruent... |
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Definition
| ...then the chords are equidistant from the center of the circle |
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| (THM 3.8.1) If two arcs of a circle have one and only one point in common... |
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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... |
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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... |
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Definition
| ...the line is perpendicular to the circle's radius at the point of contact |
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| (THM 3.8.2) If a line is not perpendicular to a circle's radius at a point of contact... |
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Definition
| ...then the line is not tangent to the circle |
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| (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... |
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Definition
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| (THM 3.8.3) If a line L passes through an interior point A of a circle... |
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Definition
| ...then the line is a secant of the circle, and thus intersects the circle at exactly two points |
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