juda521

=Chapter 9= = =

=9.1=

radius- a segment that goes from the center point of the circle to the outer rim chord- a segment whos endpoints are on the line that is the outer circle diameter- it is a chord that contains the center point of a circle semicirlce- a arc whoes endpoints are the endpoints of the diameter minor arc- a arc that is shorter than a semicircle major arc- the arc is longer then a seicircle centeral angle- a centeral angle of a circle is an angle that is in the plan of the circle intercepted arc- a arc whoes endpoints lie on the sides of the angle and whoes other points lie in the interior of the angle == =Chords and Arcs=
 * Your mission:**
 * //Define a circle and its in cahoots parts, then when your done use them in construction.//
 * //Define and use the circle and its degree measure of its arcs//.
 * //Find and use the length measure of the arcs.//
 * //Prove a theorem about chords and their intercepted arcs.//
 * Vocab:**
 * Things to know/Formulas:**
 * //**Things to know:** Radius=r, measure of the arc=M, lenght=L//
 * //**Formulas:** L=M/360(2(PIE)r)//


 * Chords and Arcs Theorem**
 * **//The converse of the Chords and Arcs Theorem://** //In a circle or in congruent circles, the chords of congruent arcs are equal or congruent.//
 * **//The Chords and Arcs Theorem://** //In a circle, or in congruent circles, the arcs of equal chords are congrunet.//

Find the lenght of the arc 1. arc AB 2. arc BC 3. arc CD 4. arc ABC 5. arc ABCDE
 * Practice Problems:**


 * Here is some real world examples:**

Picture 1: http://www.artie.com/20030908/arg-basketball-dunk-207x165-url.gif

Picture 2: http://solar.physics.montana.edu/YPOP/Spotlight/Tour/images/the_changing_sun.gif

=9.2=


 * Your mission:**

Secant- A seatcant to a circle is a line that intersects at two points. Tangent- A Tangent to a cirlce is a line in the plane of a circle that intersects at one point. point of tangency- The point where the Tangent intersects the circle.
 * //Define the words tangent and secants of circle.//
 * //Understand the concepts between tangents and certain radii of circles.//
 * //Understand the geomerty of a radius perpendicular to a chord of a circle.//
 * Vocab:**

=Tangents to circles=
 * Things to know/Formulas:**
 * //**Things to know:** Radius=r, measure of the arc=M, lenght=L//
 * //**Formulas:** L=M/360(2(PIE)r)//


 * Tangents to circles Theorems**
 * **//Tangent Theorem://** //If a line is tangent to a circle, then the 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 endpoints on the circle, then the line is tangent to the circle.//
 * //**Dans Thinking Theorem:** The perpendicular bisector of a chord passes through the center of the circle.//

** Find the measurement of the segmant point G is the center point.
 * Practice Problems:
 * 1) What is the measurement of segment GD
 * 2) What is the measurement of segment GF
 * 3) What is the measurement of segmant GC


 * Here is an example of real world examples:**

Picture 1: http://www.gpl.lib.me.us/StainGlass.jpg

Picture 2: http://www.wirednewyork.com/manhattan/columbus_circle/columbus_circle.jpg

=9.3=

inscribed angle- an angle whose vertex lies on a circle and whose sides are chords of the circle. radius- a segment that goes from the center point of the circle to the outer rim. chord- a segment whos endpoints are on the line that is the outer circle. diameter- it is a chord that contains the center point of a circle. =Inscribed Angles and Arcs=
 * Your mission:**
 * //Define inscribed angle and intercepted arc.//
 * //Develop and use the inscribed angle Theorem and its corollaries.//
 * Vocab:**
 * Things to know/formulas:**
 * //**Things to know:** Radius=r, measure of the arc=M, lenght=L//
 * //**Formulas:** L=M/360(2(PIE)r)//
 * Inscribed Angles and arcs Theorem**
 * **//Inscribed angle Theorem://** //The measure of the inscribed angle is equal to one-half the measure of the arc intercepted//
 * //**Right Angle Corollary:** If an inscribed angle interceptes a semicricle, then the angle is a right angle.//
 * //**Arc-intercept corollary:** If two inscribed angles intercept the same arc, then they have the same measurement.//


 * Practice problems:**

Find the measurements.
 * 1) Find the measurement of the arc ABC
 * 2) Find the measurement of the angle FHB
 * 3) Find the measurement of angle HIC


 * Here is some real world examples of arcs:**

Picture 1: http://www.hickerphoto.com/data/media/24/picture_of_rainbow_sc174.jpg

Picture 2: http://hematology.im.wustl.edu/stlouis/arch.jpg

=9.4=

radius- a segment that goes from the center point of the circle to the outer rim chord- a segment whos endpoints are on the line that is the outer circle diameter- it is a chord that contains the center point of a circle semicirlce- a arc whoes endpoints are the endpoints of the diameter minor arc- a arc that is shorter than a semicircle major arc- the arc is longer then a seicircle centeral angle- a centeral angle of a circle is an angle that is in the plan of the circle intercepted arc- a arc whoes endpoints lie on the sides of the angle and whoes other points lie in the interior of the angle
 * Your mission:**
 * //Define angles that are made by secants and tangents of circles.//
 * //Develop and use theorems about measures of arcs intercepted by these angles.//
 * Vocab:**

=Angles Formed by Secants and Tangents= Angles formed by Secants and Tangents Theorems**
 * Things to know/formulas:**
 * //**Things to Know**: There are 3 diffrent types of cases to classify angles with circles.//
 * //**Formulas:** X= X/2 (case 1) (X1+X2)/2 (case 2) (X1-X2)/2 (case 3)//
 * [[image:wikikikikikiikkikikikiki.JPG]]
 * **//D=an^2 Theorem://** //If a tangent and a secant or chord, intersects the circle at the point of tangency. Then the angle made comes out to be one-half of the intercept arc.//
 * //**The great Theorem:** The measure of a angle formed by two secants or chords that intersect in the interior of a circle is one-half the sum of the measures of the arcs intercepted by the angle and its vertical angle.//
 * //**The DAN:** The measure of an angle formed by two secants that intersects in the exterior of a circle is one-half the difference of the lenght of the intercepted arcs.//
 * Practice Problems:**


 * 1) Find the measurement of angle EBC
 * 2) Find the measurement of angle ABC
 * 3) Find the measurement of angle EDC
 * 4) Find the measurement of angle EBA
 * 5) Find the measurement of angle D


 * Here are some real world examples of angles formed by secants:**

Picture 1: http://www.saint-denis.culture.fr/img/sd_072.jpg

Picture 2: http://www.daytoncyo.org/basketball/basketball1.jpg = = =9.5=

Tangent segment- the segment between the point of tangency and where its intersects with another line is know as the tangent segment Secant segment- the secant intersects the circle at 2 diffrent points, the secant segment is from the intersection point of the other line to the farthes point that intersects the circle. External secant segment- it is the part of the segment that does not enter the circle. internal secant segment- It is the segment inside the circle. Chord- a segment whos endpoints are on the line that is the outer circle.
 * Your mission:**
 * //find and use special cases of segments related to circles, Include the following; secant-secant, secant-tangant, and chord-chord segments//
 * //make and use theorems about measures of the segments.//
 * Vocab:**

=Segments of Tangents, Secants, and Chords=
 * Things to know/Formulas:**
 * //**Things to know:** Radius=r, measure of the arc=M, lenght=L//
 * **//Formulas://** //L=M/360(2(PIE)r) and X= X/2 (case 1) (X1+X2)/2 (case 2) (X1-X2)/2 (case 3)//
 * Segments of Tangents, Secants, and Chords**
 * //**The Theorem that changed all Theorems:**// //If two you have two segments that are tangent to a circle from the same external point, then the two segments are the same.//
 * //**The Theorem of Math:** If two secants intersect outside a circle, then the product of the lengths of one secant segment and its external segment equals the product of the lengths of the other secant segment and its external segment.(whole x outside=whole x outside)//
 * //**The greater Theorem:** If a secant and a tangent intersect outside a circle, then the product of the lengths of the secant segment and its external secant segment equals the product of the tangent segment squared.(whole x outside =tangent squared)//
 * //**The last of the Theorems:** If two chords intersect inside a circle, then the product of the lengths of the segments of one chord equals the product of the lengths of the segments of the other chords.//
 * Practice problems:**
 * 1) What does segment DE equal
 * 2) Is line ABC congruent to line EDC


 * Here are some real world examples:**

Picture 1: http://curious.astro.cornell.edu/images/Earth_Sun_distance.gif

Picture 2: http://sunearthday.nasa.gov/2006/images/gal_006.jpg

=9.6=

Graph- A drawing representing the relationship between two sets of data, one set represented on a perpendicular scale or axis, the other on a horizontal scale or axis. The relationship is plotted where the two scales intersect, the line between meeting points generally being called the graph. y-intercept- The point in the line where the line intersects the y axis. x-intercept- The point in the line where the line intersects the x axis. (it would be good to look over the vocab from the other sections)
 * Your mission if you chose to accept:**
 * //Develop and use the amazing equation of a circle.//
 * //fix the amazing equation for a circle to move the center in the coordinate plane.//
 * Vocab:**

=Circles in the coordinate plane= Fing the radius and center point for each circle.
 * Things to Know/Formulas:**
 * //**Things to know:** in the equation x^2+y^2=(some number given to you) x and y equal zero because there is no point next to it. If it was (x-3)^2+(y+4)^2=(some number) then the point would be (**3**,-**4**). (This equation helps you form circles just in case you didnt Know). To find the radius you need to know the (some number) the radius is just that some number squared.//
 * //**Formulas:** x^2 +y^2 =(some number)//
 * Practice problems:**
 * 1) x^2+y^2 =25
 * 2) (x+4)^2+(y-6)^2=49
 * 3) (x-7)^2+(y-3)^2=100
 * 4) (x+5)^2+(y+4)^2=81


 * Here Are some real world examples:**

Picture 1: http://www.nunomira.com/blog/imagens/Firefox_Crop_Circle.jpg

Picture 2: http://www.physicsguides.com/images/deathstar.jpg

=Practice Problem Answers= 9.1
 * 1) 90 degrees
 * 2) 58 degrees
 * 3) 60 degrees
 * 4) 148 degrees
 * 5) 270 degrees

9.2
 * 1) 5.8309
 * 2) 3.5084041
 * 3) 5.8309

9.3


 * 1) 90 degrees
 * 2) 60 degrees
 * 3) 90 degrees

9.4
 * 1) 135 degrees
 * 2) 90 degrees
 * 3) 180 degrees
 * 4) 90 degrees
 * 5) 180 degrees

9.5
 * 8
 * 1) yes

9.6
 * 1) The center point is (0,0) and the radius is 5
 * 2) The center point is (-4,6) and the radius is 7
 * 3) The center point is (7,3) and the radius is 10
 * 4) The center point is (-5,-4) and the radius is 9