# Shared Flashcard Set

## Details

Geometry Vocabulary
chapters 10.1 - 10.3
35
Mathematics
03/16/2009

Term
 [image] circle
Definition
 the set of all points in a plane that are equidistant from a given point
Term
 [image] central angle
Definition
 The set of all points in a plane that areequidistant from a given point, called the center of the circle.
Term
Definition
 The distance from the center of acircle to a point on the circle. A segment whose endpoints arethe center of the circle and a point on the circle. Plural is radii.
Term
 Congruent
Definition
 Two circles that have the same radius.
Term
 [image] diameter
Definition
 A chord that passes through the center of the circle. The distance across a circle, through its center.
Term
 [image] chords
Definition
 a segment whose endpoints are points on the circle. PS A and PR Aare chords.
Term
 [image] secant
Definition
 a line that intersects a circle in two points. Line j is a secant.
Term
 tangent
Definition
 A trigonometric ratio, abbreviated as tan;a line in the plane of a circle that intersects the circle in exactly one point.
Term
 [image] tangent circles
Definition
 Circles that intersect in one point
Term
 [image] concentric
Definition
 Circles that have a common center.
Term
 [image] common tangent
Definition
 A line or segment that is tangent to two circles. A common internal tangent intersects the segmentthat joins the centers of the two circles. A common external tangent does not intersect the segment that joins the centers of the two circles.
Term
 interior of a circle
Definition
 All points of the plane that are inside a circle.
Term
 Exterior of a circle
Definition
 All points of the plane that are outside a circle.
Term
 [image] point of tangency
Definition
 The point at which a tangent line intersects the circle to which it is tangent is the point of tangency.
Term
 [image] central angles
Definition
 An angle whose vertex is the center of a circle.
Term
 [image] major arc
Definition
 Part of a circle that measures between 180° and 360°.
Term
 [image] minor arc
Definition
 Part of a circle that measures less than 180°.
Term
 semicircle
Definition
 An arc whose endpoints are the endpoints of a diameter of the circle.
Term
 [image] measure of a minor arc
Definition
 The measure of its central angle.
Term
 [image] measure of a major arc
Definition
 The difference between 360° and the measure of its associated minor arc.
Term
 [image] inscribed angle
Definition
 An angle whose vertex is on a circle and whose sides contain chords of the circle.
Term
 [image] intercepted arc
Definition
 The arc that lies in the interior of an inscribed angle and has endpoints on the angle.
Term
 inscribed
Definition
 An angle whose vertex is on a circle and whose sides contain chords of the circle.
Term
 [image]Theorem 10.1
Definition
 If a line is tangent to a circle, then it isperpendicular to the radius drawn to thepoint of tangency.
Term
 [image]Theorem 10.2
Definition
 In a plane, if a line is perpendicular to a radiusof a circle at its endpoint on the circle, then theline is tangent to the circle.
Term
 [image]Theorem 10.3
Definition
 If two segments from the same exteriorpoint are tangent to a circle, then theyare congruent.
Term
 [image]Postulate 26
Definition
 The measure of an arc formed by twoadjacent arcs is the sum of the measuresof the two arcs.
Term
 [image]Theorem 10.4
Definition
 In the same circle, or in congruent circles,two minor arcs are congruent if and only iftheir corresponding chords are congruent.
Term
 [image]Theorem 10.5
Definition
 If a diameter of a circle is perpendicularto a chord, then the diameter bisects thechord and its arc.
Term
 [image]Theorem 10.6
Definition
 If one chord is a perpendicular bisector ofanother chord, then the first chord is adiameter.
Term
 [image]Theorem 10.7
Definition
 In the same circle, or in congruent circles,two chords are congruent if and only ifthey are equidistant from the center.
Term
 [image]Theorem 10.8
Definition
 If an angle is inscribed in a circle, then its measureis half the measure of its intercepted arc.
Term
 [image]Theorem 10.9
Definition
 If two inscribed angles of a circle intercept thesame arc, then the angles are congruent.
Term
 [image]Theorem 10.10
Definition
 If a right triangle is inscribed in a circle, then thehypotenuse is a diameter of the circle. Conversely,if one side of an inscribed triangle is a diameter ofthe circle, then the triangle is a right triangle andthe angle opposite the diameter is the right angle.
Term
 [image]Theorem 10.11
Definition
 A quadrilateral can be inscribed in a circle if andonly if its opposite angles are supplementary.
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