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9.1 Chords and Arcs** __**Central Angle-**__ a cenle in the plane of a circle whose vertex is the center of the circle. __**Intercepted Arc-**__ an arc whose endpoints lie on the sides of the angle and whose other points lie in the interior of the angle is the intercepted arc of the central angle. __**Degree Of Measures-**__ the degree of measure of a minor arc is the measure of its central angle. The degree measure of a major arc is 360degree minus the degree measure of its minor arc. The degree measure of a semicircle is 180degree. __**Chord and Arc Theorem-**__ in a circle, or in congruent circles, the arcs of congruent chords are congruent. __**Converse of the Chords and Arcs Theorem-**__ in a circle, or in congruent circles, the chords of congruent arcs are congruent. http://www.mathwarehouse.com/geometry/circle/chord-perpendicular-bisector.html
 * [[image:http://www.riverclydeusers.info/images/sqwinty.jpg width="305" height="215"]]
 * Definition:** **__Circle-__** a set of all points in a plane that are equidistant from a given point in the plane known as the center of the circle.
 * __Arc Length-__** L=M/360°(2**pi**r)

Definition: __Secant-__** a secant to a circle is a line that intersects the circle at two points. __**Converse of the Tangent** **Theorem-**__ if a line is perpundicular to a radius of a circle at its endpoint on the circle, then the line is tangent to the cirlce. http://www.geom.uiuc.edu/education/math5337/monge/module-2.html
 * 9.2 Tangents to Circles
 * __Tangent-__** is a line in the plane of the circle that intersects the circle at exactly one point, which is known as the point of tangency.
 * __Tangent Theorem-__** if a line is tangent to a circle, then the line is perpundicular to a radius of the circle drawn to the point of tangency.
 * __Radius and Chord Theorem-__** a radius that is perpundicular to a chord of a circle bisects the chord.
 * __Theorem-__** the perpundicular bisector of a chord passes through the center of the circle.

Defintion: __Inscribed Angle Theorem-__** The measure of an angle inscried in a circle is equal to one-half the measure of the intercepted arc. http://www.geom.uiuc.edu/~dwiggins/conj44.html
 * 9.3 Inscribed** **Angles and Arcs
 * __Right Angle Corollary-__** If an inscribed angle intercepts a semicircle, then the angle is a right angle.
 * __Arc-Intercept Corollary-__** If two inscribed angles intercept the same arc, then they have the same measure.

__**Theorem-**__ The measure of a secant-tangent angle with its vertex outside the ircle is one-half the difference of the measure of the intercepted arcs. __**Theorem-**__ The measure of a tangent-tangent angle with its vertex outside the circle is one-half the difference of the measures of the intercepted arcs. or the measure of the major arc minus 180°.
 * 9.4 Angles Formed by Secants and Tangents**
 * Definition: __Theorem-__** If a tangent and a secant (or chord) intersect on a circle at the point of tangency, then the measure of the angle formed is one-half the measure of its intercepted arc.
 * __Theorem-__** The measure of an angle formed by two secants or chords that intersect in the interior of a circle is one-half the sum of the measures of the arcs intercepted by the angle and its vertical angle.
 * __Theorem-__** The measure of an angle formed by two secants the intersect in the exterior of a circle is one-half the difference of the intercepted arcs.

__**Theorem-**__ If two secants intersect outside a circle, then the product of the lengths of one secant segment and its external segment equals the product of the lenths of the other secant segment and its external segment. (whole x outside = whole outside) __**Theorem-**__ If a secant and a tangent intersect outside a circle, then the product of the lengths of the secant segment and its external segment equals the lenght of the tangent segment squared. (whole x outside = tangent squared) __**Theorem-**__ If two chords intersect inside a circle, then the product of the lengths of the segment of one chord equals the product of the lengths of the segments of the other chord. http://www.mathwarehouse.com/geometry/circle/product-segments-chords.php
 * 9.5 Segments of Tangents, Secants, and Chords**
 * Definition: __Theorem-__** If two segments are tangent to a circle from the same external point, then the segments of are of equal length.

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 * 9.6 Circles in the Coordinate Plane