Geometry Chapter 10 Circles Flash Cards
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30 terms
Terms | Definitions |
|---|---|
 circle | the set of all points in a plane that are equidistant from a given poing, called the center of the circle. |
| chord | a segment whose endpoints are on the circle. |
| diameter | a chord that passes through a center and the other endpoints is on the circle. |
| radius | a segment where one endpoint is at the center and the other endpoint is on the circle. |
| tangent | a line that intersects a circle at exactly on point. |
| point of tangency | the exact point the lines intersects the circle. |
| secant | a line that intersects a circle at 2 points |
| common tangent | a line that is tangent to 2 circles |
| common external tangent | a common tangent that does not intersect the segment that joins the centers of the circles. |
| common internal tangent | a common tangent that intersects the segment that joings the centers of the circles. |
| concentric | two circles that share the same center. |
| congruent circles | two circles that have congruent diameters fo congruent radii. |
| theorem 10.1 | in a plane, a line is tangent to a cirlce if and only if the line is perpendicular to a radius of the circle at its endpoint on the circle. |
| theorem 10.2 | tangent segments from a common external points are congruent. |
| central angle | an angle whose vertex is the center of a circle. |
| minor arc | if the measure of angle APB is less than 180 degrees, then the portion of the circle included between points A and B form this |
| major arc | this starts and ends with points A and B but it is the arc that lies in the exterior of angle APB. |
| semicircle | an arc whose endpoints are the endpoints of a diameter. its measure is always 180. |
| measure of a minor arc | is the measure of its central angle. |
| measure of a major arc | the difference between 360 and the measure of the related minor arc. |
| arc addition postulate | the measure of an arc formed by two adjacent arcs is the sum of the measures of the 2 arcs |
| congruent arcs | the arcs are congruent if they have the same measure and they are arcs of the same circle or of congruent circles. |
| theorem 10.3 | in the same circle, or in congruent circles, 2 minor arcs are congruent if and only if their corresponding chords are congruent. |
| theorem 10.4 | if one chord is a perpendicular bisector of another chord, then the first chord is a diameter. |
| theorem 10.5 | if a diameter of a circle is perpendicular to a chord then the diameter bisects the chord and its arcs. |
| theorem 10.6 | 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 arb | the arc that lies in the interior of an inscribed angle and has endpoints on the angle. |
| theorem 10.7 | the measure of an inscribed angle is one half the measure of its intercepted arc. |
| theorem 10.8 | if 2 inscribed angles of a circle intercept the same arc, then the angles are congruent. |
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