chre118

Section 9.1

-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. __CIRCLE:__ 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. __RADIUS:__ a segement from the center of the circle to a point on the circle. __CHORD:__ a segment whos endpoints line on a circle. __DIAMETER:__ a chord that contains the center of a circle. __ARC:__ an unbroken part of a circle. __ENDPOINTS:__ the points of an arc. __SEMICIRCLE:__ an arc whose endpoints are endpoints of a diameter. __MINOR ARC:__ an arc that is shorter than a semicircle of that circle. __MAJOR ARC:__ an arc that is longer than a semicircle of that circle. __CENTERAL 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. __DEGREE MEASURE OF ARCS:__ the measure of its central angle. the degree measure of a major arc is 360 degrees minus the degree measure of its minor arc.**
 * __OBJECTIVES__
 * __ARC LENGTH:__**
 * L=M/360(2 pie r)**

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**
 * __OBJECTIVES:__

a line that intersects the circle at two points.** a line in the plane of the circle that intersects the circle at exactly oen point, which si known as the point of tangency. THEOREM:__ the perpendicular bisector of a chord passes through the center of the circle.**
 * __SECANT:__
 * __TANGENT:

section 9.3

-define //inscribed angle// and //intercepted angle//**
 * __OBEJECTIVES:__
 * -develope and use the inscribed angle theorem and its corollaries**



an angle whose vertex lies on a circle and whose sides are chords of the circle.** if an inscribed angle intercepts a semicircle, then the angle is a right angle** if two inscribed circles have the same arc, then they have the same measure.**
 * __INSCRIBED ANGLE:__
 * __RIGHT ANGLE COROLLARY:__
 * __ARC INTERCEPT COROLLARY:__

section 9.4

-define angles formed by secants and tangents of circles -develop and use theorems about measures of arcs intercepted by these angles.**
 * __OBJECTIVES:__



1. vertex is on the circle. 2. vertex is inside the circle. 3.vertex is outside the circle.**
 * __3 different cases:__

section 9.5



-define special cases of segements related to circles, including secant-secant, secant-tangent, and chord-chord segements. -develop and use theorems about measures of the segement.
 * __OBJECTIVES:__

__TANGENT SEGEMENT

SECANT SEGEMENT

EXTERNAL SECANT SEGEMENT

CHORD__**

-If two segements are tangent to a circle from the same external point, then the segements are equal -If two secants intersect outside a circle, the product of the lengths of one secant segement and its external segement equals the product of the lengths of the other secant segement and its external segement -If a secant and a tangent intersect outside a circle, then the product of the lengths of the secant segement and its external segement equals the lengths of the other secant segement and its external segements -If two chrods intersect inside a circle, then the product of the lengths** **of the segement of one chord equals the length of the other segement.**
 * __THEOREMS:__

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:__

__DERIVING THE EQUATION OF A CIRCLE:__ x²+y²=r²** (x-h)²+(y-k)²=r²**
 * __MOVING THE CENTER OF THE CIRCLE:__