# Shared Flashcard Set

## Details

Geometry: 3.8
Definitions and results from section 3.8
57
Mathematics
11/28/2016

Term
 Definition of Circle
Definition
 The set of points in a plane that lies at a positive fixed distance from some specific point.
Term
Definition
 The positive fixed distance from each point lying on the circle to the circle's center.
Term
 Definition of interior point
Definition
 For point P and circle O with radius r, if OP < r, then P is an _______ to circle O
Term
 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 of distance
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.
Term
 Definition of equidistant
Definition
 A point is __________ from two lines iff the distances from the point to each of the two lines are equal.
Term
 Definition: The set of points in a plane that lies at a positive fixed distance from some specific point.
Definition
 Circle
Term
 Definition: The positive fixed distance from each point lying on the circle to the circle's center.
Definition
Term
 Definition: For point P and circle O with radius r, if OP < r, then P is an _______ to circle O
Definition
 interior point
Term
 Definition: For point P and circle O with radius r, if OP > r, then P is an _______ to circle O
Definition
 exterior point
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.
Definition
 distance
Term
 Definition: A point is __________ from two lines iff the distances from the point to each of the two lines are equal.
Definition
 equidistant
Term
 Illustration of Chord
Definition
 [image]
Term
 Illustration of Secant
Definition
 [image]
Term
 Illustration of Diameter
Definition
 [image]
Term
 Illustration of Central angle
Definition
 [image]
Term
 Illustration of Inscribed angle
Definition
 [image]
Term
 Illustration of Tangent
Definition
 [image]
Term
 Illustration of Subtended arc of an angle
Definition
 [image]
Term
 Illustration of Angle inscribed in a semicricle
Definition
 [image]
Term
 [image]
Definition
 Chord
Term
 [image]
Definition
 Secant
Term
 [image]
Definition
 Diameter
Term
 [image]
Definition
 Central angle
Term
 [image]
Definition
 Inscribed angle
Term
 [image]
Definition
 Tangent
Term
 [image]
Definition
 Subtended arc of an angle
Term
 [image]
Definition
 Angle inscribed in a semicricle
Term
 Definition of Minor Arc
Definition
 The intersection of a circle with the interior points of a central angle
Term
 Definition: The intersection of a circle with the interior points of a central angle
Definition
 Minor Arc
Term
 Definition of Semicircle
Definition
 Intersection of a circle and the closed half plane lying on one side of a diameter of the circle
Term
 Definition: Intersection of a circle and the closed half plane lying on one side of a diameter of the circle
Definition
 Semicircle
Term
 Definition of Major arc
Definition
 Intersection of a circle with the exterior points of a central angle
Term
 Definition: Intersection of a circle with the exterior points of a central angle
Definition
 Major arc
Term
 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
Term
 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 of Secant
Definition
 A line that meets a circle in two distinct points
Term
 A line that meets a circle in two distinct points
Definition
 Secant
Term
 Definition of Tangent
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
 subtend
Term
 A chord is said to _______ an arc iff the intersection between the arc and the chord is the end points of the arc.
Definition
 subtend
Term
 If two chords have the same measure, then they are _________ (definition).
Definition
 congruent
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
Term
 (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
Term
 (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
 ...d(x) is continuous.
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
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