Keha517

=CHAPTER 9=

9.1 Chords and Arcs:
__OBJECTIVES:__
 * to define a circle and its parts relating to it, and use them to construct a circle.
 * define and use the degree measures of arcs.
 * define and use the length measures of arcs.
 * learn a theorem about chords and their intersecting arcs and prove it.

this is a site i found it tells you all the vocab you will learn is this part of the chapter and includes pictures to help you understand it. [|VOCAB&PICS]. this show some of the things you will learn: GREEN-radius RED-are both chords BLUE-tangent to the circle
 * VOCAB:**
 * CENTRAL ANGLE-is an angle in the same plane as the circle whose vertex is the center of the circle.
 * INTERCEPTED ARC- an arc that has endpoints that lie on the sides of the angle and has another point that lie in the interior of the angle
 * DEGREE MEASURE OF ARCS-
 * 1) minor arc:the measure of its central angle.
 * 2) major arc:360 minus the degree measure of its minor arc.
 * 3) degree of a semicircle is 180.


 * __EQUATIONS__:**

L=M/360 (2*pi*r)
L=length M=degree measure or an arc of the circle r = radius**
 * pi=pi or 3.14

9.2 Tangents to Circles:
__OBJECTIVES__:
 * learn the definition of tangents and secants of circles.
 * learn and understand what relationship there is between tangents and certain radii of a circle.
 * understand the math between the radius perpendicular to the chord of the circle


 * VOCAB**:
 * SECANT LINE- is when the line crosses through the circle on the inside and touches the edge of the circle twice. (not the diameter)
 * TANGENT LINE- is a line that does not cross through the circle and only touches the edge of the circle once. mainly is just a straight line that is on the side of a circle. Where the line touches the edge of the circle is called the point of tangency.

__**THEOREMS**__:
 * __tangent theorem__-If a line is tangent to a circle then the line is __?__ to a radius of the circle drawn to te point of tangency.
 * __Radius and chord theorem__-a radius that is perpendicular to a chord of a circle __?__ the chord.
 * __converse of the tangent theorem__- if a line is perpendicular to a radius of a circle at its endpoint on the circle then the line is __?__ to the circle.

9.3 Inscribed Angles and Arcs:
__OBJECTIVES:__
 * define incribed angle and intercepted arc.
 * develope and use the inscribed angle theorem and its corollaries.


 * VOCAB:**
 * INSCRIBED ANGLE- an angle whose vertex lies on a circle and whose sides are chords of the circle.

__**THEOREMS:**__ __Inscribed angle theorem__- the measure of an angle inscribed in a circle is equal to the measure of the intercepted arc.

//2results of that theorem://
 * 1) RIGHT-ANGLE COROLLARY: If an inscribed angle intercepts a semicircle, then the angle is a right angle.
 * 2) ARC-ANGLE COROLLARY: If two inscribed angles interrcept the same arc, them they have the same measure.

9.4 Angles Formed by Secants and Tangents:
__OBJECTIVES:__
 * define angles formed by secants and tangents of circles.
 * develop and use theorems about measures of arcs intercepted by these angles


 * CASES:**

1.vertex is on the circle-
 * secant and tangent
 * two secants

2.vertex is inside the circle-
 * two secants

3.vertex is outside the circle-
 * two tangents
 * two secants
 * secant and tangent


 * __THEOREMS:__**
 * if a tangent and a secant (or chord) intersect on a circle at the point of tangency, tehn the measure of the angle formed is __?__ the measure of its intercepted arc.
 * the measure of an angle formed by two secants or chords that intersect in the interior of a circle is __?__ the __?__ of the measures of the arcs intercepted by the angle and its vertical angle.
 * the measure of an angle formed by two secants that intersect in the exterior of a circle is __?__ the __?__ of the measures of the intercepted arcs.

9.5 Segments of Tangents, secants, and chords:
__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.


 * THEOREMS:**
 * if there is TWO tangents they are equal in length.
 * if there is TWO secants there is a equation to find the length of the segments. **W * O = W * O**


 * if there is ONE secant and ONE tangent there is an equation to find the length of each segment. **W * O = T ²**
 * if there is TWO chords there is an equation to find the length of the segments. **Pt1 * Pt2 = Pt1 * Pt2**

W=whole O=outside T=tangent Pt=part

9.6 circles in the coordinate plane:
__EQUATIONS:__

For a circle with center at origin: this means that the center is on (0,0)
 * X ² + Y² = r²**

__**Example:**__ center-(0,0) radius-5 x² +y² =5² x² +y² =25 r =? r ² =25 square root of 25 =5 r = 5

For a circle with center not at origin: this means the center is every where EXCEPT (0,0)
 * ( x - h )² + ( y - k )² = r²**

__**Example:**__ center-(5,4) = (h,k) radius- 3

( x-5) ² + ( y-4 ) ² = 3 ²



if the cordinates for the center of the circle are negative the math changes to the opposite ( like from + to - or - to + )
 * __*IMPORTANT__**

[|SOME EXAMPLES AND HELP.]