Geometry Chapter 10 -10.5
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Created by:
Selena53 on April 19, 2011
Subjects:
geo, geometry, chapter 10, chapter, mcdougal, holt, holt mcdougal, larson, larson geometry, 10, ten, properties, of, circles
Classes:
Cheney Lesson, Quest Academy 8th Grade Flashcards
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40 terms
Terms | Definitions |
|---|---|
 circle | set of all points in a plane that are equidistant from a given point |
| center | the point that all points on a circle are equidistant to |
| radius | a segment whose endpoints are the center and any point on the circle |
| chord | a segment whose endpoints are on a circle |
| diameter | a chord that contains the center of the circle |
| secant | a line that intersects a circle in two points |
| tangent | a line, segment, or ray in the plane of a circle that intersects the circle in exactly one point |
| point of tangency | the one point where the tangent intersects the circle |
| tangent circles | coplanar circles that intersect in one point |
| concentric circles | coplanar circles that have a common center |
| common tangent | a line, ray, or segment that is tangent to two coplanar circles |
| Perpendicular Radius to a Tangent Theorem | In a plane, a line is tangent to a circle if and only if the line is perpendicular to a radius of the circle at its endpoint on the circle. |
| Congruent Tangents to External Point Theorem | Tangent segments from a common external points are congruent. |
| central angle | an angle whose vertex is the center of the circle |
| minor arc | an arc of a circle whose measure is less than 180 degrees |
| major arc | an arc of a circle whose measure is more than 180 degrees |
| semicircle | an arc with endpoints that are the endpoints of a diameter |
| measure of a minor arc | measure of its central angle |
| measure of a major arc | 360-measure of related minor arc |
| measure of a semicircle | 180 |
| arc addition postulate | The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs. |
| congruent circles | circles with the same radius |
| congruent arcs | arcs with the same measure that are part of the same circle or of congruent circles |
| Congruent Corresponding Chords and Minor Arcs Theorem | In the same circle, or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent. |
| Perpendicular Bisecting Chords & Arcs Theorem | If one chord is a perpendicular bisector of another chord, then the first chord is a diameter. |
| Perpendicular Bisecting Chords & Arcs Converse | If a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc. |
| Equidistant Congruent Chords from the Center Theorem | In the same circle, or in congruent circles, two chords are congruent if and only if they are equidistant from the center. |
| inscribed angle | an angle whose vertex is on a circle and whose sides contain chords of the circle |
| intercepted arc | the arc that lies in the interior of an inscribed angle and has endpoints on the angle |
| Measure of an Inscribed Angle Theorem | The measure of an inscribed angle is one half the measure of its intercepted arc. |
| Congruent Inscribed Angles with the Same Arc Theorem | If two inscribed angles of a circle intercept the same arc, then the angles are congruent. |
| Hypotenuse of an Inscribed Right Triangle is a Diameter Theorem | If a right triangle is inscribed in a circle, then the hypotenuse is a diameter of the circle. |
| Hypotenuse of an Inscribed Right Triangle is a Diameter Converse | If one side of an inscribed triangle is a diameter of the circle, then the triangle is a right triangle and the angle opposite the diameter is the right angle. |
| Supplementary Opposite Angles in an Inscribed Quadrilateral Theorem | A quadrilateral can be inscribed in a circle if and only if its opposite angles are supplementary. |
| segments of a chord | when two chords intercept in the interior of a circle, each chord is divided into two segments that are called... |
| Segments of a Chord Theorem | If two chords intersect in the interior of a circle, then the product of the lengths of the segments of one chord is equal to the products of the lengths of the segments of the other chord. |
| Segments of Secants Theorem | If two secant segments share the same endpoint outside a circle, then the product of the lengths of one secant segment and one external segment equals the product of the lengths of the other secant segment and its external segment. |
| Segments of Secants and Tangents Theorem | If a secant segment and a tangent segment share an endpoint outside a circle, then the product of the lengths of the secant segment and its external segments equals the square of the length of the tangent segment. |
| standard equation of a circle | (x-h)² + (y-k)² = r² Center: (h,k) |
| simple equation of a circle | x² + y² = r² |
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