duan521

=Chapter 9= = =

9.1 Chords and Arcs
Define and use the degree measure of arcs. Define and use the length measure of arcs. Prove a theorem about chords and their intercepted arcs. [|Link] Circle-** The set of all points in a plane that are equidistant from a given point in the plane known as the middle of the circle. L = M over 360(2pi//r//)
 * Objectives:** Define a circle and its associated parts, and use them in constructions.
 * __//Definitions://__
 * Radius-** A segment from the center of the circle to a point on the circle.
 * Diameter-** A diameter is a chord that contains the center of a circle.
 * Arc-** An unbroken part of a circle.
 * Endpoints-** The points that divide the circle in 2 arcs.
 * Semicircle-** an arc whose endpoints are endpoints of a diameter.
 * Minor arc-** an arc that is shorter than the semicircle.
 * major arc-** an arc that is longer than the semicircle.
 * Central Angle-** An angle in the plane of the 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.
 * Degree Measure of Arcs-** The degree measure of a minor arc is the measure of its central angle. The degree measure of a major arc is 360 degrees minus the degree measure of its minor arc.
 * Arc Length-** If //r// is the radius off a circle and M is the degree of measure of an arc of the circle, then the length which is L, of an arc is given by the following:
 * Chords and Arcs Theorem-** In a circle the arcs of conguent chords are congruent.
 * The Converse of the Chords and Arcs Theorem-** In a congruent or in a regular circle, the chords of congruent arcs are the same.

9.2 Tangents to Circles
Understand the relationship between tangents and certain radii of circles. Understand the geometry of a radius perpendicular to a chord of a circle.
 * Objectives:** Define tangents and secants of circles.

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Secants and Tangents-** A secant to a circle is a line that intersects the circle at two points. A tangent is a line that is on the plane of the circle and intersects at one point. This point is called the **point of tangency. Tangent Theorem-** If a line is a tangent to a circle, then the line is secant to a radius of the circle drawn to the point of tangency.
 * //__Definitions:__//
 * Radius and Chord Theorem-** A radius that is perpendicular to a single chord of the circle intersects the chord.
 * Converse of the Tangent Theorem-** If a line is perpendicular to a radius of a circle then the line is equal to the circle.
 * Theorem-** The perpendicular bisector of a chord passes through the middle of the circle.

9.3 Inscribed Angle Theorem
Develop and use the Inscribed Angle Theorem and its corollaries.
 * Objectives:** Define inscibed angle and intercepted arc.

Inscibed angle-** An angle whose vertex lies on a circle and whose sides are chords of the circle.
 * //__Definitions:__//
 * Inscibed Angle Theorem-** The degree of measure of an angle inscribed in a circle is equal to half the measure of the arc that is intercepted.
 * Right-Angle Corollary-** If a semi-circle is intercepted by an inscribed angle, then it is a right angle.
 * Arc-Intercept Corollary-** If an arc is intercepted by two inscibed angles, then they have the same measure.

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9.4 Angles formed by Secants and Tangents
Develop and use theorems about measures of arcs intercepted by these angles. [|LNK] Theorem #1-** If a tangent and a secant intersect on a circle at the point of tangency, then the measure of the angle formed is twice the measure of the arc that was intercepted.
 * Objectives:** Define angles formed by secants and tangents of circles.
 * //__Definitions:__//
 * Theorem #2-** The measure of an angle formed by two secants or chords that intersect in the inside of a circle is twice the mength of the measures of the arcs intercepted by the angle and its vertical angle.
 * Theorem #3-** The measure of an angle that is formed by 2 secants that intersect the exterior of a circle is double the length of the measures of the intercepted arcs.
 * Theorem #4-** The measure of a secant-tangent angle with its vertex on the outside of the circle is
 * Theorem #5-** The measure of a tangent-tangent angle with its vertex outside of the circle is

9.5 Segments of Tangents, Secants, and Chords
Develop and use theorems about measures of the segments. [|Link] Theorem #1-** If two segments are tangent to a circle and they come from the same external point, then the segments are equal. (Whole times Outside = Whole times Outside)
 * Objectives:** Define special cases of segments related to circles, including, secant- tangent, secant-secant, and chord-chord.
 * //__Definitions:__//
 * Theorem #2-** If two secants intersect out of a circle, the answer of the lengths of one secant segment and its external segment equals
 * Theorem #3-** If a secant and a tangent intersect outside of a circle the the answer of the lengths of the secant segment and its external segment equals (Whole times Outside = Tangent Squared)
 * Theorem #4-** If two chords intersect on the inside of the circle, the the answer of the lengths of the segments of one chord is

9.6 Circles in the Coordinate Plane
Adjust the equation for a circle to move the center in a coordinate plane.
 * Objectives:** Develop and use the equation of a circle.

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External Links

http://www.kidsites.com/sites-edu/math.htm

http://www.eduplace.com/math/brain/

http://mathforum.org/dr.math/

http://www.aplusmath.com/