miwi218

Chapter 9 - Chords and arcs 9.1-** Chords and arcs
 * [[image:graff_copy.jpg]]©

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http://arxiv.org/PS_cache/math/pdf/0701/0701791v1.pdf link to further info.

circle- a figure in which all sets of points are equal distance from the center point in a plane. radius- a segment from the center of the circle to a point on the circle. chord- a segment whose endpoints line on a circle diameter- is a chord that contains the center of a circle

arc- an unbroken part of a circle semi circle- Is an arc whose endpoints are endpoints of a diameter. minor arc- of a circle is an arc that is shorter than a semi circle of that of a circle. is named by endpoints. major arc-is an arc that is longer than a semicircle of that of a circle. Named by the endpoints and another point that lies on the arc.
 * major and minor arcs*

© central angle- an angle in the plane of a circle whose vertex is the center of that circle. degree measure of an arc-The degree measure of a minor arc is the measure of its central angle.The degree measure of a major arc is 360 degrees minus the degree measure of its minor arc. The degree measure of a semi circle is 180 degrees.
 * degree measure of arcs*


 * 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/360d(2(pi)r)

Tangents to circles http://www.clarku.edu/~djoyce/trig/angle.html link for more info.
 * 9.2-**
 * secants and tangents*

Secant- is the line that intersects the circle at two points. Tangent- a line in the plane of a circle that intersects the circle at exactly one point. © Tangent theorem- If a line is tangent to a circle, then the line is to a radius of the circle drawn to the point of tangency.

Radius ans chord theorem- A radius that is perpendicular to a chord of a circle the chord

Converse of the tangent 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.

Inscribed angle theorem
 * 9.3-**


 * The inscribed angle theorem*

inscribed angle- An angle whose 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 equal to the measure of the intercepted arc.


 * Two results of the Inscribed angle theorem*

Right angle collary- If an inscribed angle intercepts a semicircle, then the angle is a right angle.

Arc-intercept collary- If two inscribed angles intercept the same arc,then they have the same measure. blue line is major arc,black is semi circle, and pink is minor arc.©

http://en.wikipedia.org/wiki/Image:Inscribed_angle_theorem.svg -for more info

Angles formed by secants and tangents.
 * 9.4-**

case1-vertex is on the circle. case2-vertex is inside the circle. case3-vertex is outside the circle. © 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 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 the of the measures of the arcs intercepted by the angle and its vertical angle.

Theorem-The measure of a secant-tangent angle with its vertex outside the circle is.

Theorem- The measure of a tangent-tangent angle with its vertex outside the circle is. http://regentsprep.org/regents/mathb/5A1/CircleAngles.htm more info

Segments of tangents,secants, and chords.
 * 9.5**

theorem-If two segments are tangent to a circle from the same exter**nal point**, then the segments.

theorem- If two secants intersect outside a circle,the product of the lengths of one secant segment and its external segments equal. (wholeXoutsideX=wholeXoutside)

Theorem- 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. (wholeXoutside=Tangent squared) © Theorem- If two chords intersect inside a circle then the products of the lengths of the segments of one chord equals.


 * 9.6**

Circles in the coordinate plane. ©

Graphing a circle from an equation.

equation 1 x^2 +y^2=r^2

http://tutorial.math.lamar.edu/AllBrowsers/1314/Circles.asp -more info

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