Frst607+Chapter+9+link

__Chapter 9__

 * [[image:http://i78.photobucket.com/albums/j98/steph9790/mathwiki.gif?t=1179352236 link="http://s78.photobucket.com/albums/j98/steph9790/?action=view&current=mathwiki.gif"]] .** [[image:http://farm1.static.flickr.com/164/363989684_c960c67d8b.jpg?v? width="102" height="140" link="http://flickr.com/photos/33732557@N00/363989684/"]]If you click the picture of the clock you will be directed to the website it was found and on the picture it will have little captions of alot of the vocab through out chapter 9.

__9.1--CHORDS__ AND __ARCS__
Radius-Is a segment from the center of the circle to a point on the circle. M/360 ((2)(pi)(r)) EXAMPLE- picture made by me.
 * Objectives-**
 * Define a circle and its associated parts, and use them in contructions.
 * Define and use the degree measure of arcs.
 * Define and use the length of measure of arcs.
 * Prove a theorem about the chords and their intercepted arcs.
 * Vocab-**
 * Circle**-A circle is 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.
 * Chord**-Is a 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 angle in the plane of a circle whose vertex ist he center of the circle.
 * Intercepted Arc**- An arc whose endpoints lie on the sides of the angle and whose other ponits lie in the interior of the angle is the intercepted arc of the central angle.
 * Degree Measure of Arcs**- The degree measure of a minor arc is the measure of its central angle. The degree measure of a major arc is 360 degrees minus the degree measure of its minor arc. The degree measure of a semicircle is 180 degrees.
 * 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, the chords of congruent arcs are congruent.
 * Arc length Formula**-- L

__9.2 TANGENTS TO CIRCLES.__
Secants**-A secant to a circle is a line that intersects the circle at two points. TANGENT.
 * Objectives-**
 * Define tagents 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.
 * Vocab-
 * Tangent**- is a line in the plane of the circle that intersects the circle at exactly one point which is known as the point of tangency.
 * 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.
 * Theorem**- The perpendicular bisector of a chord passes through the center of the circle.

__9.3 Inscribed Angles and Arcs__
Inscribed Angle Theorem**- The measure of an angle inscribed in a circle is equal to one-half the measure of the intercepted arc. EXAMPLE- if arc PB=37 what is angle X ? SOLUTION-- **Look at the inscribed angle theorem it is equal to HALF the measure of the intercepted arc....the arc is 37degrees 37/2=18.5**
 * Objectives-**
 * Define inscribed angle and intercepted arc.
 * Develop and use the Inscribed Angle Theorem and its corollaries.
 * Vocab-
 * Right-Angle Corollary**- If an inscribed angle intercepts a semicircle, then the angle is a right angle.
 * Arc-Intercepted Corollary**- If two inscribed angles intercept the same arc, then they have the same measure.

__9.4 Angles formed by Secants and Tangents__
Theorem 1**- If a tangent and a secant (or a chord) intersect on a circle at the point of tangency, then the measure of the angle formed is one-half the measure of its intercepted arc. EXAMPLE- Angle HQG is formed by two secants that intersect inside the circle
 * Objectives-**
 * Define angles formed by secants and tangents of circles.
 * Develop and use theorems about measures of arcs interrcepted by these angles.
 * Vocab-
 * Theorem 2**- The measure of an 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 angles.
 * Theorem 3**- The measure of an angle formed by two secants that intersect in the exterior of a circle is one-half the difference of the measures of the intercepted arcs.
 * Theorem 4-**The measure of a secant-tangent angle with its vertex outside the circle is one-half the difference of the measures of the intercepted arcs.
 * Theorem 5-**The measure of a tangent-secant angle with its vertex outside the circle is one-half the difference of the measures of the intercepted arcs, or the measure of the major arc minus 180.

measure HQG =1/2(arcHG= arcEF)= 1/2(100+50)=150degrees.

__9.5 Segments of Tangents, Secants, and Chords__
Vocab- EXAMPLE-- In this figure AX=0.26, IW=00.91 and NI=0.27, find IB 0.26•0.91=0.27•XB 0.27•XB=0.2366 XB is about 0.88**
 * 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.
 * Theorem 1**- If two segments are tangent to a circle from the same external point, then the segments are of equal lengths
 * Theorem 2**- If two secants intersect outside a circle, the product of the lengths of one secant segment and its external segment equals the length of the tangent segment squared. (Whole x Outside = Whole x Outside)
 * Theorem 3**- If a secant and a tangent intersect outside a circle, then the product of the lengths of the secant segment and its external segment equals the length of the tangent segment squared. (Whole x Outside = Tangent Squared)
 * Theorem 4**- 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 chord.
 * RI•IW=NI•IB

__9.6 Circles in the Coordinate Plane__
EXAMPLES-- When the center of the origin is X^2+Y^2=36 ANSWER**.. It would be (0,0) ANSWER...** it would be 6 because the square root of 36 is 6. Moving The Center of the Circle-- EXAMPLE (X+5)^2+(Y-4)^2=144 What is the Center of origin?** What would the radius be?
 * Objectives**
 * Develop and use the equation of a circle.
 * Adjust the equation for a circle to move the center in a coordinate plane.
 * Questions A**
 * What is the center of the origin?
 * What would the radius be?
 * Questions B-
 * ANSWER..**it would be (-5,4) because you take the opposite of the numbers.
 * ANSWER..** it would be 12, because 12 is the square root of 144.

**pretend this is the circle but its cropped with the graph on it to realize the center is (0,0) and the radius is 6. This pic. corresponds with questions A.**

pictures--
 * All the EXAMPLES of pictures for the chapter were made by Me.

Links that will help you understand more of this chapter below-- To help understand vocab.-- http://regentsprep.org/regents/mathb/5A1/CircleAngles.htm http://www.math.com/tables/geometry/circles.htm More on Circle Theorems http://www.mathsrevision.net/gcse/pages.php?page=13 This website below you have to explore a bit. There are more than just the 1st page of information on Angle arc relationships http://my.nctm.org/eresources/view_article.asp?article_id=7077**