GIJO29

=Chapter 9=

-Define a circle 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.
 * 9.1 Chords and Arcs**
 * Objectives**

__Circle__- the set of all points in a plane that are equidstant from a given point in the plane know as the center of the circle. __Radius__- a segment from the center of the circle to a point on the circle __Chord__- a segment whose endpoints lay on s circle __Diameter__- a chord that contains the center of a circle __Arc__- a unbroken part of a circle __Endpoints__- any two distinct points on a circle divide the circle into two arcs __Semi Circle__- an arc whose endpoints are the endpoints of a diameter __Minor Arc__- A minor arc of a circle is an arc that is shorter than a semicircle of that circle __Major Arc__- A major arc of a circle is an arc that is longer than a semicircle of that 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 __Degree Measure of Arcs__- the measure of its central angle. Th degree measure of a major arc is 360° minus the degree measure f its minor arc. the degree measure of a semicircle is 180°
 * Definitions**

__Arc Length__ L = M / 360° (2 x Pi x R) //R// is the radius of a circle, //M// is the degree measure of an arc of the circle and //L// is the length, the arc is given by: __Chords and Arcs Theorem__ In a circle, or in congruent circles, the arcs of congruent chords are congruent __The Converse of the Chords and Arcs Theorem__ In a circle or in congruent circles, the chords of congruent arcs are congruent
 * Theorems**

-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
 * 9.2 Tangents to Circles**
 * Objectives**

__Secant__- line that intersects the circle at two points __Tangent__**-** line in theplane of the circle that intersects the circle at exactly one point __Point of tangency__**-** the point a tangent intersects a circle
 * Definitions**

__Tangent theorem__ If a line is tangent to a circle then te line is perpendicular to a radius of the circle drawn to the 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 endpoint on circle then the line is tangent to the circle __Theorem__ The perpendicular bisector of a cord just passes through the center of the circle
 * Theorems**

Objectives -**Define inscribed angle and intercepted arc. -Develop and se the Inscribed Angle Theorem and its corollaries.
 * 9.3 Inscribed Angles and Arcs

__Inscribed Angle__- an angle whose vertex lies on a cirlce and whose sides are chords of the circle __Intercepted Arc__- an arc whose endpoints le on the sides of an inscribed angle
 * Definitions**

__Inscribed Angle Theorem__ The measure of an inscribed is equal to half the measure of the intercepted arc __Right Angle Corollary__ If an inscribed angle intercepts a simicircle, then the angle is a right angle __Arc-Intercepted Corollary__ If two inscribed angles intercept the same arc, then they have the same measure Objectives -**Define angles fromed by secants and tangents to circles. -Develop and use theorems abiyt measures of arcs intercepted by these angles.
 * Theorems**
 * 9.4 Angles Formed by Secants and Tangents


 * Definitions**