noel325

= = =//CHAPTER 9//=


 * **Objective 1-** Define a circle and its associated parts, and use them in constructions.
 * **Objective 2-** Define and use the degree measure of arcs.
 * **Objective 3-** Define and use the length measure of arcs.
 * **Objective 4-** Prove a theorem about chords and their intercepted arcs.

//__Vocabulary to Know:__//

 * Circle-** A circle is a set of all points on a plane that are equidistant from a given point in the plane known as the center of the circle.
 * Radius-** A radius is segment from the center of the circle to a point on the circle.
 * Chord-** A chord is a segment whose endpoints line on a circle.
 * Diameter-** A diameter is a chord that contains the center of a circle.
 * Arc-** An arc is an unbroken part of the circle
 * Endpoints-** Any two distinct points on a circle divide the circle into two arcs. Those two points are known as the endpoints.
 * Semicircle-** A semicircle is an arc whose endpoints are the endpoints of a diameter.
 * Major Arc-** A major arc of a circle is an arc that is longer than a semicircle of that circle.
 * Minor Arc-** A minor arc of a circle is an arc that is shorter than a semicircle of that circle.
 * Central Angle-** A central anle of a circle is an angle in the plane of the circle whose vertex is the center of the circle.
 * Intercepted Arc-** An arc whose endponts lie on the sides of the angle and whose other points lie in the interior of the angle.


 * Degree Measures 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. The degree measure of a semicircle is 180 Degrees.

(//Measure=//m//)// mRT=100 degrees mTS=90 degrees //(Arc=Capital letters)// RT and TS, which have just one endpoint in common, are called adjacent arcs. Add their measures to find the measure of RTS. mRTS=mRT+mTS=100 degrees + 90 degrees = 190 degrees
 * Example 1:** Find the measures of arcs RT,TS, and RTS.
 * Solution-** The measures of arcs RT and TS are found from their central angles.
 * Example 2:** Find the length of the indicated arc. Express your answer to the nearest millimeter. (There are 20 equal sectors on a dartboard.)
 * Solution-** (The Radius of the circle is 170 mm) The length of the arc is 1/20 of the circumference of the circle. Remember that C=2x3.14xr Length of arc 1/20[(2x3.14)x170] 17x3.14 = 53.4 = __53 mm__

L= (M/360)(2x3.14xr)
 * Arc Length:** If the radius is //r// and //M// is the degree measure of an arc of the circle, then the length, //L//, of the arc is given by the following:


 * Chords and Arcs Theorems:** In a circle, or in congruent circles, the arcs of congruent chords are congruent.

LESSON 9.2 Tangents to Circles

 * **Objective 1-**
 * **Objective 2-**
 * **Objective 3-**

//__Vocabulary to Know:__//
Tangent- Point of Tangency- Tangent Theorem: Radius and Chord Theorem: Example: Converse of Tangent Theorem:**
 * Secant-

LESSON 9.3 Inscribed Angles and Arcs

 * **Objective 1-**
 * **Objective 2-**

//__Vocabulary to Know:__//
Inscribed Angle Theorem: Example 1: Right angle Corollary: Arc-Intercept Corollary: Example 2: Example 3:**
 * Inscribed Angle-

LESSON 9.4 Angles Formed by Secants and Tangents
Case 2- Case 3- Vertex On Circle-Secant and Tangent Theorem(Case 1): Vertex Inside Circle-Two Secants Theorem (Case2): Vertex Outside Circle- Two Secants (Case 3): Example 1: Example 2:**
 * **Objective 1-**
 * **Objective 2-**
 * Case 1-

LESSON 9.5 Segments of Tangents, Secants and Chords

 * **Objective 1-**
 * **Objective 2-**

//__Vocabulary to Know:__//
Secant Segment- External Secant- Chord- Segments Formed by Tangents Theorem: Segments Formed by Secants Theorem A: Segments Formed by Secants Theorem B: Segments Formed by Interesting Chords Theorem: Example 1: Example 2: Example 3: Example 4: Example 5:**
 * Tangent Segment-

LESSON 9.6 Circles on the Coordinate Plane
Example 2:**
 * **Objective 1-**
 * **Objective 2-**
 * Example 1: