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=Chapter 9=

9.1 **__Chords and Arcs__**

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.
 * Definition:
 * Central Angle -** is an angle in the plane of a circle whose vertex is the center of the circle.
 * Intercepted Arc -** an arc whose endpoints lie on the sides of the angle and whose other points lie in the interior of the angle is the intercepted arc of the central angle
 * Chord -** is a segment whose endpoints line on a circle
 * Arc -** is an unbroken part of a circle
 * Semi-circle -** is an arc whose endpoints are endpoints of a diameter
 * Minor arc -** is an arc that is shorter than a semi-circle of that circle
 * Major arc -** is an arc that is longer than a semi-circle of that circle

__**Arc Length formula**__ L = M/360 (2(pi)r)

9.2 **__Tangents to Circles__

Definitions: Secant -** is a line that intersects the circle at two points
 * Tangent -** is a line in the plane of the circle that intersects the circle at exactly one point

9.3 **__Inscribed Angles and Arcs__

Picture taken from Flickr.com

Inscribed Angle -** is an angle whose vertex lies on a circle and whose sides are chords of the circle http://mathworld.wolfram.com/InscribedAngle.html


 * Inscribed Angle** **Theorem -** the measure of an angle inscribed in a circle is equal to 1/2 the measure of the intercepted arc
 * Right Angle Corollary -** if an inscribed angle intercepts a semicircle, then the angle is a right angle
 * Arc-Intercept Corollary -** If two inscribed angles intercept the same arc, then they have the same measure

9.4 **__Angles Formed by Secants and Tangents__

Theorem:** - 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 1/2 the measure of its intercepted arc

Here are some examples of secants, tangents, and chords http://www.algebralab.org/lessons/lesson.aspx?file=Geometry_CircleSecantTangent.xml an example of two secants that meet outside of the circle

http://www.algebralab.org/lessons/lesson.aspx?file=Geometry_CircleSecantTangent.xml an example of a secant and tangent - More info and pictures can be found on this [|WEBSITE]

9.5 **Segments of Tangents, Secants, and Chords

Theorem: -** If two segments are tangent to a circle from the same external point, the segments are congruent [|**http://www.partnership.mmu.ac.uk/cme/Geometry/CircleGeom/Images/Tangent.jpg**]

Segments formed by intersecting chords. http://wwwy.mathwarehouse.com/geometry/circle/images/product-of-chords/product-chords-segments-picture.gif
 * Theorem:** If two chords intersect inside a circle, then the product of the lengths of the segments of one chord equals the product of the length of the other chord

Segments formed by secants. http://www.mathwarehouse.com/geometry/circle/images/two-secants/example-problem.gif
 * Theorem**: If two secants intersect outside a circle, the product of the lengths of one secant segment and its external segment equals the other secant segment.