grda328

9.1//**Objectives: Define a circle and its associated parts, and use them in constructions.**// //__Circle__//: A circle is the set of all points in a plane that are equidistant from a given point on the plane known as the center of the circle. //__Radius__//: A segment from the center of the circle to any one point on the circle. //__Chord__//: A segment whose endpoints line on a circle. //__Diameter__//: a chord that contains the center of a circle //__Central Angle__//: An angle 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. The degree measure of a minor arc is the measure of it's central angle. The degree measure of a major arc is 360 minus the degree measure of it's minor arc. The degree measure of a semicircle is 180. If //r// is the radius of a circle and M is the degree measure of an arc of the circle, then the length, L, of the arc is given by the following: L=M/360(2(3.14)//r//) In a circle, or in congruent circles, the arcs of congruent chords are congruent.
 * //Define and us the degree measure of arcs.//**
 * //Define and use the lengt//h measure of arcs.**
 * //Prove a theorem about chords and their intercepted arcs.//**
 * Degree Measure of Arcs**
 * Arc Length**
 * Chords and Arcs Theorem**

=9.2= Understand the geometry of a radius perpendicular to a chord of a circle.// Secants and Tangents** //__Secant__**:**// A line that intersects the circle at two points. //__Tangent__**:**// A line in the plane of a circle that intersects the circle at exactly one point. If a line is tangent to a circle, then the line is sinilar to a radius of the circle drawn to the point of tangency. A radius that is perpendicular to a chord of a circle the chord. If a line is perpendicular to a radius of a circle at its endpoint on the circle, then the line is to the circle. The perpendicular bisector of a chord passes throught the center of a circle.
 * //Objectives: Define tangen//ts and secants of circles.**
 * //Understand the relatipnship between tangents and certain radii of circles
 * Tangent Theorem:[[image:9-2.JPG align="right"]]**
 * Radius and Chord Theorem**
 * Converse of the Tangent Theorem**
 * Theorem**

=9.3= Develop and use the Inscribed Angle Theorem and it's corollaries.//** __Inscribed Angle__: An angles whose vertex lies on a circle and whose sides are chords of the circle. The measure of an angle inscribed in a circle is equal to HALF the measure of the intercepted arc. If an inscribed angle intercepts a semicircle, then the angle is a right angle. If two inscribed angles intercept the same arc, then they have the same measure.
 * //Objectives: Describe inscribed angle and intercepted arc.
 * Inscribed Angle Theorem[[image:9-3.JPG align="right"]]**
 * Right Angle Corollary**
 * Arc-Intercept Corollary**

=9.4= Develop and use theorems about measures of arcs intercepted by these angles.//** If a tangent and a secant (or a chord) intersect on a circle at the point of tangency, then the measure of the angle formed is HALF the measure of it's intercepted arc. The measure of an angle formed by two secants or chords that intersect in the interior of a circle is The measure of an angle formed ny two secants that intersect in the exterior of a circle The measure of a secant-tangent angle with it's vertex outside the circle is half the intresected arc. The measure of a tangent-tangent angle with it's vertex outside the circle is Big Arc-Small Arc=Angle Measure.
 * //Objectives: Define angles formed by secants and tangents of circles.
 * Theorem**
 * Theorem**
 * Theorem**
 * Theorem**
 * Theorem**

=9.5= //Develop and use theorems about measures of the segments.// Theorem** If two secants are tangent to a circle from the same external point, then the segments are equal. If two secants intersect outside a circle, the product of the lengths of one secant segment and it's external segment equals //(WholexOutside=WholexOutside)// If a secant and a tangent intersect outside a circle, then the product of the lengths of the secant segment and it's external segment equals //(WholexOutside=Tangent Squared)// If two chords intersect inside a circle, then the product of the lenths of the segments of one chord equals
 * //Objectives: Define special cases of segments related to circles, including secant-secant, secant-tangent, and chord-chord segments.//
 * Theorem**
 * Theorem**
 * Theorem**

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