wiri323

//Chapter// 9

__Section 9.1__ •Define a cirlce and its associated parts, and use them in constructions. •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.
 * Objectives:**

//Definition: circle// •A circle is the set of all points in a plane that are equidistant from a given point in the plane known as the center of the circle. A **radius** is a segment from the center of the circle to a point on the circle. A **chord** is a segment whose endpoints line on a circle. A **diameter** is a chord that contains the center of a circle. a half-circle. A semicircle is named by its endpoints and another point the lies on the arc. A minor arc is named by its endpoints. A major arc is named by its endpoints and another point that lies on the arc.
 * Blue Boxes/Definitions**
 * Arc-** An arc is an unbroken part of a circle.
 * Endpoints-** Any two distinct points on a circle divide the circle into two arcs. the points are called endpoints.
 * Semicircle-** A semicircle is an arc whose endpoints are endpoints of a diameter. A semicircle is informally called
 * Minor arc-** A minor arc of a circle is an arc that is shorter then a semi circle of that circle.
 * Major arc-** A major arc of a circle is an arc that is longer than a semicircle of that circle.

//Definitions: Central angle and intercepted arc •//A **central angle** of a cirlce is and angle in the plane of a circle whose vertex if the center of the circle. An arc whose endpoints lie on the sides of the angle and whose other points lie in the interior of the angle if the **intercepted arc** of the central angle.

//Definition: Degree measure of arcs// •The degree measure of a mior 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. The degree measure of a semicircle is 180 degrees. //Arc Length.// •If R is the radius of a circle and M is the degree measure of a arc of the circle, then the length of the arc is given by the following: L=M/360 (2(3.14)R) //Chords and Arcs Theorem.// In a circle, or in congruent circles, the arcs of congruent chords are equal. //The converse of the chords and arcs theorem.// In a circle or in congruent circles, the chords of congruent arcs are equal.

__Section 9.2__ •Define tangents and secants of circles. •Understand the relationship between tangents and certain radii of circles. •Understand the geometry of a radius perpendicular to a chord of a circle. //Secants and Tangents.// •A **secant** to a circle is a line that intersects the circle at two points. A **tangent** is a line in the plane of the circle that intersects the circle at exactly one point, which is known as the //Tangent Theorem.// •If a line is tangent to a circle, then the line is perpendicular to a radius of the circle drawn to the point of tangency.
 * Objectives:**
 * Blue Boxes/Definitions**
 * point of tangency.**

//Radius and Chord theorem.// •A radius that is perpendicular to a chord of a circle bisects the chord. //Converse of the tangent theorem. •//If a line is perpendicular to a radius of a circle at its end point on the circle, then the line is _ to the circle.

//Theorem.// •The perendicular bisector of a chord passes through the center of the circle.

__Section 9.3__ •Define inscribed angle and intercepted arc. •Develop and use the inscribed angle theorem and its corollaries.
 * Objectives:**

whose sides are chords of the circle.
 * Blue Boxes/Definitions**
 * Inscribed angle-** An inscribed angle is an angle whose vertex lies on a circle and

//Inscribed angle theorem.// •The measure of an angle inscribed in a circle is equal to _ the measure of the intercepted arc. //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. __Section 9.4__ •Define angles formed by secants and tangents of cirlces. •Develop and use theorems about measures of arcs intercepted by these angles.
 * Objectives:**

//Theorem// •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 its intercepted arc. //Theorem// •The measure of an angle formed by two secants of chords that intersect in the interior of a circle is 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 that intersect in the exterior of a circle is half of the measures of the intercepted arcs.

//Theorem// •The measure of a secant-secant angle wih its vertex outside the circle is half of the difference of the intercepted arcs.

//Theorem// •The measure of a tangent-tangent angle with its vertex outside the circle is half of the difference of the intercepted arcs.

__Section 9.5__ •Define special cases of segments related to circles, including secant-secant, secant-tangent, and chord-chord segments. •Develop and use theorems about measures of the segements.
 * Objectives:**

//Theorem// •If two segments are tangent to a circle from the same external point, then the segments

//Theorem// •If two secants intersect outside a circle, the product of the lengths of one secant segment and its external segment equals (whole • 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 __.__ (whole • outside = tangent sqaured)

//Theorem// •If two chords intersect inside a circle, then the product of the lengths of the segments of one chord equals

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