shasam

=__Chapter 9__=

9.1
a set of all points that are in a plane and are all an equal distance fro the point in the center of the circle.
 * Circle:**



a line that goes from point of circle to point inside of circle. The radius ends halfway across circle.
 * Radius:**

__for example:__ this bike wheel shows a radius with it connecting to the wheel.



a line the goes from one point on the circle, to ending point on the circle, through the center of the circle. Just like in the peace sign, the line going straight down through the middle is a diameter.
 * Diameter:**



A segmant with endpoints line on a circle.
 * Chord:**

An unbroken part of the circle.
 * Arc:**

has the same endpoints as a diameter. also known as a half circle. __example:__ like the moon when only half of it is showing.
 * Semicircle:**



circle of arc is smaller than a semicirlce. about a fourth of a circle.
 * Minor Arc:**

circle of arc is bigger than semicircle. about three fourths of a circle.
 * Major Arc:**

an angle with the vertex being the center of the circle.
 * Central Angle:**

the points are in the interior angle of the central angle.
 * Intercepted Arc:**

degree measure of a major arc is 360° minus the degree measure of its minor arc. degree measure of a semicircle is 180°.
 * Degree Measure of Arcs:**

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...
 * Arc Length:**

//L// = M/360° (2(pi)//r//)

__example:__



In a circle, or in congruent circles, the arcs of congruent chords are congruent.
 * Chords and Arcs Theorem:**

In a circle or in congruent circles, the chords of congruent arcs are perpendicular.
 * The Converse of the Chords and Arcs Theorem:**

9.2
a line that goes through a circle at two different points on the circle.
 * Secant:**

a line that runs through the outside of the circle and hits only one point.
 * Tangent:**

__example:__ this is what it would look like.

If a line is tangent to a circle, then the line is to a radius of the circle drawn to the point of tangency.
 * Tangent Theorem:**

A radius that is perpendicular to a chord of a circle the chord.
 * Radius and Chord Theorem:**

If a line is perpendicular to a radius of a circle at its endpoint on the circle, then the line is to the circle.
 * Converse of the Tangent Theorem:**

The perpendicular bisector of a chord passes through the center of the circle.
 * Theorem:**

9.3
vertexs are in the circle at differnt points. the sides are a circles chords.
 * Inscribed Angle:**

The measure of an angle inscribed in a circle is equal to one half the measure of the intercepted arc.
 * Inscribed Angle Theorem:**

a right angle that that had the inscribed angle intercept with the semicircle.
 * Right Angle Corollary:**

__example:__

two inscribed angles intercept have the same arc and the same measure.
 * Arc-Incercept Corollary:**

__example:__

9.4
two lines coming off of one point on circle. could be a tangent and secant or two secants.
 * Vertex is on circle:**



or



like an X through the circle, has two secants.
 * Vertex is inside circle:**

starting point not on circle or in circle. two lines come off and form secants.
 * Vertex is outside circle:**

__for example:__ the blue line outside the nob is like a vertex outside a circle.

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 half the measure of its intercepted arc.
 * Theorem:**

The measure of an angle formed by two secants or chords that intersect in the interior of a circle is half of the sum of the measures of the arcs intercepted by the angle and its vertcal angle.
 * Theorem:**

The measure of an angle formed by two secants that intersect in the exterior of a circle is half the distances of the measures of the intercepted arcs.
 * Theorem:**

The measure of a secant-tangent angle with its vertex outside the circle is one half the distance of the measures of the intercepted arcs.
 * Theorem:**

The measure of a tangent-tangent angle with its vertex outside the circle is one half the distance of the measures of the intercepted arcs, or the measure of the major arc minus 180°.
 * Theorem:**

9.5
__examples of:__ Tangent Segmant is XA

Secant Segment is XB

External Secant Segment is XC

A line that goes through two different points of the circle.
 * Chord is BC**

If two segmants are tangent to a circle from the same external point, then the segments are the same size.
 * Theorem:**

If two secants intersect outside a circle, the product of the lengths of one secant segmant and its external segmant equals the product of the lengths of the other secant segment and its external segment. (whole x outside = whole x outside)
 * Theorem:**

If a secant and a tangent intersect outside a circle, then the product of the lengths of the secant segmant and its external segmant equals the length of the tangent. (whole x outside = tangent squared)
 * 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 lengths of the segments of the other chord.
 * Theorem:**

9.6

 * Center not at origin:**

Center: (0,2) Radius: 2


 * Equation:** x^2+(y-2)^2=4