aram530

Chapter 9
 * 9.1**

Chords and Arcs


 * Define a circle and its associated parts and use htem in constructions.
 * Define and use the degree measure of arcs
 * Define and use the lengh measure if arcs
 * Prove a theorem about chords and their intercepted arcs
 * Circle**-the set of points in a plane that are equildistant form a given point in the plane known as the center of the circle.
 * Radius**- is a segment for the center of the circle to a point on the circle
 * Chord**- segment whose endpoints line on a circle
 * Diameter**- is a chord that contains the center of a circle
 * Central angle**- of a circle is an angel in the plabe of a circlewhos vertex is the center of the circle.
 * Intercepted arc**- an arc whos end points lie on the sides of hte angle and whose other points lie in the interior of the angle is the intercepted arc of the central angle.

FORMUALS

arc length- if r is the radius of a cirlce 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*3.14r)

9.2 - define tangents and secants of circles - understand the relationship between tangents and cetain radii of cirlces - understand the geometry of a radios perependicular to a chord of a circle

SECANT- a circle is a line that intersects the circle at two points TANGENT- is a line in the plane of the circle that intersects the circle at exactly one point POINT OF TANGENCY- the intersection refered to above

Thoerem-the perpendicular bisector of a chord passes through the center of the circle.

9.3 INSCRIBED ANGEL- is and angle whose vertex lies of a circel and whose sides are chords of the circle. RIGHT ANGLE COROLLARY- if and iscribed ange interceots a semicircle, then the angle is a right angle. ARC-INTERCPET COROLLARY-if two inscribed angles intercept the same arc, then they have the same measure.

9.4

Objectives- -define Angles formed by secants and tangents of circles. -develop and use theorems about measures of arcs intercepted by three angles.

9.5

Objectives- -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 segments.

9.6

Objectives- -develop and use the equation of a circle. -adjust the equation for a circle to move the center in a coordinate plane.