Chapter+9+page+by+Joel+S.

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=Circles= ==

9.1 Chords and Arcs
= = = = Example L=20 R=15 (2pi*15) = 147.89 20*360= 7200 7200/147.89=48.68 M=48.68
 * Circle-**set of all points in a plane that are equidstant from a point in the plane called the center of the circle.
 * Radius-**segment from the center to a point on the edge of the circle
 * Chord-**segment whose endpoints lay on the edge of the circle
 * Diameter-**chord that passses through the center of a circle
 * Arc-**the outer part on the edge of the circle; unbroken
 * Endpoints-**two points on a circle dividing the circle into two arcs
 * Semi-circle-**arc, the endpoints are that of a diameter
 * Minor arc-**arce that is shorter than a semi-circle(diameter)
 * Major arc-**arc that is longer than a semi-circle(diameter)
 * Intercepted arc-**where the endpoints lie on the sides of the angle and other points lie in the interior of the angle.
 * Degree measure of arcs-** **minor arc** is the measure of its central angle.**Major arc** is 360 degrees minus the degree measure of its minor arc. The degree meausre of a semicircle is 180 degrees.
 * Arc Length-**If //r// is the radius of a circle and //M// is the degree measure of an arc of the circle, then the length, //L//, of the arc is given by the following: L=M/360 degrees (2//PIEr//)

**9.2 Tangents to Circles [[image:9.22.JPG width="474" height="276"]]**

 * Secant-**is a line that intersects the circle at two points
 * Tangent-**intersects the circle at exatly one point; called the point of tangency
 * Point of Tangency-**where the tangent intersects the circle at.
 * Tangent Theorem-**a line is tangent to a circle, then the line is perpendicular to the radius of the cirle drawn to the point of tangency

**9.3 Inscribed Angles and Arcs[[image:circle33.png link="http://en.wikipedia.org/wiki/Image:CIRCLE_LINES.svg"]]**
example
 * Inscribed angle-**This is an angle wose vertex lies on a circle and whose sides are chords of the circle
 * Inscribed Angle Theorem-**The measure of an angle inscribed in a circle is equl to half the measure of the intercepter arc
 * Right angle corollar-**inscribed angle intercepts a semi circle; the angle is a right angle
 * Arc intercept Corollar-**two inscribed angles intercept the same arc; they have the same measure

If a tangent and a secent or chord intersect on a circle at the point of tangency, the measure of the angle formed is half the measure of its intercepted arc
 * 9.4 Angles Formed by Secants and Tangents**

The measure of an angle formed by two secants or chords that intersects in the interior of a circle is half the sum of the measures of the arcs intercepted by the angle and its vertical angle X1*X2/2

The Measure of an angle formed by two secants that intersect in the exterior of a circle is half the difference of the measure of the intercepted arcs X1*X2/2

If two segments are tangent to a circle from the same external point, then the segments are equal Line BD and BC are equal
 * 9.5 Segments of Tangents Secants and Chords**

If two secants intersect outside a circle, the product of the lengths of on secant segment and its external equals two secants

w*o=w*o Example If segment AC is 20 and EC is 5, BD is 5 what is DE? 20*5=25*x 100=25x 100/25=25x/25 X=4

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 one secant and 1 tangent w*o=t^2

If two chords intersect inside a circle, then the product of the lengths of the segments of one chord equals two chords (pt1)*(pt2)=pt1*pt2

Example AX is 10, XC is 10 BX is 10, XD is unknown 10*10=10*x 100=10x 100/10=10x/10 X=10
 * 9.6 Circles in the Coordinate Plane**

X^2+y^2=16 radius=4 after you have found the x and y you need to graph it it will look something like this;

once you find the 4 points your done EX 2 (x-3)^2+(y-8)^2=100 using the standerd equation (x-h)^2+(y-k)^2=r^2 your center points should be (3,8) and radius of 10

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