foaa626

=chapter 9=

9.1 chords and arcs.
define a circle and it's assocatied parts and use them in constructions difine and use the degree measure of arcs. define and use the length measure of arcs** .a-b an arc =Circle=
 * objectives

http://www.windowseat.ca/circles/ = = =**9.2 tangents to circles**= obectives define tangent and secant of a circle.
 * **origin: the center of the circle**
 * **radius: the distance from the center of a circle to any point on it.**
 * **diameter: the longest distance from one end of a circle to the other. Diamter = 2.radius**
 * **circumference: the distance around the circle.**
 * **π - pi: number equal to 3.141., that is (the circumference) (the diameter) of any circle.**
 * **arc: a curved line that is part of the circumference of a circle. The arc of a circle is measured in degrees. The whole arc of the circle is 360°**
 * **chord: a line segment within a circle that touches 2 points on the circle.**
 * **sector:is like a slice of pie (a circle wedge).**
 * **tangent::of circle: a line perpendicular to the radius that touches ONLY one point on the circle.**
 * **endpoint:**
 * **chord arc theorem: in a circle or a congruent circle to a point or acircle.**
 * **central circle : a central circle in a plane of a circlewhose vertex is the center of the circle.**
 * **circle:a sate ofall pointsin a plane that are equidstant from a given points in the plane known as the center of the circle.**
 * [[image:http://farm1.static.flickr.com/219/490825705_c986538999.jpg?v=0 width="317" height="174" align="right"]]

understand the realation ship between tangent and certain radii of the circle.

understand the geometry of raduis perpandiclar to chord of a circle. Terms

tangent line on a circle. secant- to a circle is a line the intersecs the circle at two points tangent- A LINE IN A PLANE. POINTS OF TANGENT-a LINE IN THE PLANE OF A CIRCLE THE INTERSETS THE CIRCLE AT EXACLY ONE POINT.

TANGENT THEOREM- IF A LINE IS TANGENT TO A CIRCLE THEN THE LINE LINE IS PERPENDICLAR TO A RADUIS OF ARC.

RADIUS AND CHORD THEOREM -A RADIUS THAT IS PERPNDICLAR TO A CHORD OF A CIRCLE BISECTS THE CHORD.

convers of tangent theorem-if a line perpendiclar to a radius of a circle at its point on the circle, then the line is tangent to a circle. Theorem- the perpendiclar bisector a chord passes though the center of the circle.**

http://www.coolmath.com/graphit/index.html =9.3 iscribed angles and arcs= another arc

inscirbed angles and arcs Terms inscribed angles whose vertexs lies on the circle and whose sides are chords of the circle.

right angle corallary- if an inscribed angle intersecpts an semicircle, then the angle is a right angle.

arc intrepects corallary-if two inscribed angles intercts same arc, then the have same measuer.

http://www.teachers.ash.org.au/jeather/maths/dictionary.html = = = = = = = = = = = = = = = = = = = = = = = = =9.4Angles formed by secant and tangent= secant and tangent lines.
 * objectives:[[image:http://farm1.static.flickr.com/164/363989684_c960c67d8b.jpg?v=0 width="236" height="229" align="left"]]

definiton for angles formed by secants and tangents of a circle.

learn and use theormes use in this chapter .** =Theorms:=


 * Vertex on circle-secant and tangent theorem- If a secant and a tangent line intersect on a circle at the point of tangency, then the measure of the angle formed is one-half the measureof its intercepted arc.

Vertex inside circle-two secants theorem-The masure of an angle formed by two secants or two chords that intersect in the interior part of a circle is one-half teh sum of the measures of the arcs intercepted by the angle and its vertiacl angle.

vertex outside circle-two secants theorem- An angle with a measure formed by two secants that intersect the exterior part of a circle is one-half the difference of the measures of the intercepting arcs

Theorem 4- A secant-tangent angle that has measures and also with its vertex outside the circle is one-half the difference of the measures of the intercepted arcs.

Theorem 5- A tangent-tangent angle with a measure and also with its vertex outside the circle is one-half the difference of the intercepted arcs, or the major arcs measure minus 180°. it all has something to do with this chapter** = = =9.5=

One secant, one tangent: w*o=t2
===Two Chords: p+1*p+2=p+1-p+2=== > **objections > Develope and use the equation of a circle. > Adjust the equation for a circle to move the center in a coodinate plane. > Equations: > X^2 + Y^2 = r^2 > (x - h)^2 + (y - k)^2 = r^2** = =
 * =9.6 Circles in the Coordinate Plane=
 * =9.6 Circles in the Coordinate Plane=
 * =9.6 Circles in the Coordinate Plane=
 * =9.6 Circles in the Coordinate Plane=
 * =9.6 Circles in the Coordinate Plane=
 * =9.6 Circles in the Coordinate Plane=
 * =9.6 Circles in the Coordinate Plane=
 * =9.6 Circles in the Coordinate Plane=
 * =9.6 Circles in the Coordinate Plane=
 * =9.6 Circles in the Coordinate Plane=
 * =9.6 Circles in the Coordinate Plane=
 * =9.6 Circles in the Coordinate Plane=
 * =9.6 Circles in the Coordinate Plane=
 * =9.6 Circles in the Coordinate Plane=
 * =9.6 Circles in the Coordinate Plane=
 * =9.6 Circles in the Coordinate Plane=
 * =9.6 Circles in the Coordinate Plane=
 * =9.6 Circles in the Coordinate Plane=
 * =9.6 Circles in the Coordinate Plane=
 * =9.6 Circles in the Coordinate Plane=
 * =9.6 Circles in the Coordinate Plane=
 * =9.6 Circles in the Coordinate Plane=
 * =9.6 Circles in the Coordinate Plane=
 * =9.6 Circles in the Coordinate Plane=
 * =9.6 Circles in the Coordinate Plane=
 * =9.6 Circles in the Coordinate Plane=
 * =9.6 Circles in the Coordinate Plane=
 * =9.6 Circles in the Coordinate Plane=
 * =9.6 Circles in the Coordinate Plane=
 * =9.6 Circles in the Coordinate Plane=
 * =9.6 Circles in the Coordinate Plane=
 * =9.6 Circles in the Coordinate Plane=
 * =9.6 Circles in the Coordinate Plane=
 * =9.6 Circles in the Coordinate Plane=
 * =9.6 Circles in the Coordinate Plane=
 * =9.6 Circles in the Coordinate Plane=
 * =9.6 Circles in the Coordinate Plane=
 * =9.6 Circles in the Coordinate Plane=
 * =9.6 Circles in the Coordinate Plane=
 * =9.6 Circles in the Coordinate Plane=
 * =9.6 Circles in the Coordinate Plane=
 * =9.6 Circles in the Coordinate Plane=
 * =9.6 Circles in the Coordinate Plane=
 * http://www.webmath.org/gcircle.html