pean327


 * Chapter 9

9.1 Chords and Arcs** Definitions__ Circle** __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. __radius__- Is a segment from the center of the circle to a point on the circle __chord__- Is a segment whose endpoints line on a circle. __diameter__- Is a chord that contains the center of a circle. __arc__- Is an unbroken part of the circle. __semicircle__- Is an arc whose endpoints are endpoints of a diameter. __minor arc__- Of a circle is an arc that is shorter than a semicircle of that circle __major arc__- Of a circle is an arc tha is no longer than a semicircle of that circle. if R is the radius of a circle and M is the dergre**e** measure of an arc of the circle, then the lenght L of the arc is given by the folloing: L=m/360(2 3.14 r)
 * __[[image:circulo_cagado.jpg]][[image:popa.jpg link="http://http://flickr.com/photo_zoom.gne?id=304723381&size=o"]]
 * Arc**
 * arc lenght**

__Definitions__** __secant-__ To a circle is a line that intersects the circle at two points. __tangent-__ Is a line in the plane of the circle that intesects the circle at exaclty one point which is known as the **point of tangency.**
 * 9.2 Tangents to circles

** An inscribed angle is an angle whose vertex lies on a circle and whose sides are chords of the circle. __Right angle corollary__- If an inscribed angle intercepts a semicircle, then the angle is a right agle. __Arc intercept corollary__- If two inscribed angles intercept the same arc, then they have the same measure.
 * 9.3 Inscribed angles and arcs

Angles formes by pairs of lines that intersect a circle in two or more places can be studied systematically. There are three cases to consider, according to the placement of the vertex of the angles. a)Secant and tangent b)Two secants a)Two tangents b)Two secants c)Secant and tangent
 * 9.4 Angles formed by secants and tangents**
 * Case 1**: vertex ison the circle
 * Case 2**: Vertex is inside the circle
 * Two secants
 * Case 3**: Vertex is outside the circle

__XA__ is a tagent segment. __XB__ is a secant segment. __XC__ is an external secant segment. __BC__ is a chord
 * 9.5 Segments of tangents, Secants, and chords**


 * 9.6 Circles in the coordinate plane**