dora131

http://go.hrw.com/activities/frameset.html?main=2614.html <-- 9.1 HELP
 * 9.1 Chords and Arcs**


 * __Definitions of a Circle~__**
 * Radius**-a straight line extending from the center of a circle
 * Diameter**- a straight line passing through the center of a circle
 * Chord**- the line segment between two points on a given curve.




 * __Definitions: Central Angle and Intercepted Arc~__**
 * Central angle-** an angle formed at the center of a circle by two radii
 * Intercepted arc**- an arc whose endpoints lie on the sides of the angle and whose other points lie on the sides of the angle and whose other points lie in the interior of the angle

Arc Length- L=M/360degrees(2 π r) Arc length= 6=2/360degrees (2 π 3) 6= 180 (18.84) 6=3391.2 Arc length=565.2
 * __Definition: Degree Measure of Arcs~__**
 * Example:**

http://go.hrw.com/activities/frameset.html?main=2631.html <--- 9.2 HELP**
 * 9.2 Tangents to Circle*

line or tangent segment
 * __Secants and Tangents__**
 * Secant**-one intersecting a curve at two or more points
 * Tangent-** touching at a single point, as a tangent in relation to a curve or surface
 * Point of Tangency-** The point of intersection between a circle and its tangent
 * Tangent Theorem-** a line that is tangent to a circle and the line is perpendicular to a radius of the circle drawn to the point
 * 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

Example: a=2 b=4 c=x 2**2 + 42 = x2** 4+15=**x2** 19=**x2** 4.35 = x
 * a2 + b2 = c2**

http://go.hrw.com/activities/frameset.html?main=2634.html <--9.3 HELP**
 * 9.3 Inscribed Angles and Arcs*


 * Inscribed angles-** are always equal and are formed when two secant lines of a circle intersect on the circle

http://www.ies.co.jp/math/java/geo/enshukaku/enshukaku.html <--- Dont understand inscribed angles? Here's some help!


 * [[image:http://library.thinkquest.org/20991/media/geo_cia.gif width="222" height="205"]]

Right- Angle Corollary-** if an inscribed angle intercepts a semicircle, then the angle is right angle


 * Arc- Intercept Corollary-** If two inscribed angles intercept the same arc, then they have the same measure

The inside is half the side as the outside angle so... if the inside angle was 30 the outside would be 60
 * Example:**

http://go.hrw.com/activities/frameset.html?main=2635.html <--- 9.4 HELP
 * 9.4 Angles Formed by Secants and Tangents***


 * Theorem-** If a tangent and a secant 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


 * Theorem-** the measure of and angle formed by two secants or chord that intersect in the interior of a circle is one-half the sum of the measure of the arcs intercepted by the angle and its vertical


 * Theorem-** The measure of an angle formed by two secants that intersect in the exterior of a circle is one-half the difference of the measure of the intercepted arcs

60+50/2 110/2= 55 degrees
 * Example:**

http://go.hrw.com/activities/frameset.html?main=2634.html<-- 9.5 HELP
 * 9.5 Segments of Tangents, Secants, and Chords*****


 * Tangent Segment-** a segment with one endpoint at the point of tangency of a circle and the other endpoint on the tangent line


 * Secant Segment-** A segment with one endpoint on a circle, the other endpoint at a fixed point outside the circle, and one point of intersection with the circle, not including its endpoint
 * [[image:http://img.sparknotes.com/figures/B/bc520655c299866d34385c463a8e56f8/sectansegment.gif]]

Chord-**the line segment between two points on a given curve.


 * Theorem-** If two segments share tangent to a circle from the same external point, then the segments are of equal length


 * Theorem-** If two secants intersect outside a circle, the product of the lengths of one secant segment and its external segment equals the product of the lengths of the other secants segments and its external segment (Whole X Outside =Whole X Outside)


 * Theorem-** If a secant and a tangent intersect outside a circle, the product of the lengths of the secant segment and its external segment equals the length of the tangent segment squared

FIND- HX EX * GX* FX* HX 1.31 * .45 = 1.46 * HX 1.46* HX = .5895 HX=.40
 * Example:**

FIND- XB AX *XC= DX*XB .27*.91= .27* XB .27* XB= .2366 XB= .88
 * Example2:**

http://go.hrw.com/activities/frameset.html?main=2638.html <--9.6 HELP Example:** If (8,7) the center of the orgin (x-h)2 + (y-k)2 =r (x+8)2 + (y-7)2 = 12
 * 9.6 Circles in the Coordinate Plane*

x**2**+ y**2**= r**2
 * Example2:

(3,12) r= 5 (x-3)+ (y-12)= 5
 * Example3:**

http://www.cut-the-knot.org/pythagoras/index.shtml <-- Learn more about the pythagorean theorem http://cte.jhu.edu/techacademy/web/2000/heal/siteslist.htm <--- Fun Geometry Games!