clde317

=Chapter 9=

Section 1-Chords and Arcs
__**Objectives**__ Define a circle and its associated parts, and use them in constructions Define and use the degree measure of arcs Define and use the length measure of arcs Prove a theorem about chords and their intercepted arcs

__**Definitions**__ a circle is a set of all points in a plane that are a set distance from a given point. segment from center of circle to a given point. is a segment whose endpoints lie on a circle. is a chord that intersects the center of the circle. is an unbroken part of a circle. is an arc whose endpoints are endpoints of the diameter. is an arc that is shorter than 180 degrees. is an arc longer than 180 Degrees. is an angle in the plane of a circle whose vertex is the center of the circle. is an arc whose endpoints lie on the sides of the angle and whose other points lie in the interior of the angle. The degree of a minor arc is the measure of its central angle. The degree measure of a major arc is 360° minus the degree measure of its minor arc. The degree of a semicircle is 180°. CB is the intercepted arc of central angle CPB. Find measure of angle APB if APC is 95 and angle CPB is 85. they are found from their central angles. All you have to do is ad 95 and 85 to find the whole angle.... which is 180 degrees. [|photo from flickr.com] [|Chords and Arcs web site.] Do the problems on the bottom of the page after reading the info.
 * Circle**-
 * Radius**-
 * Chord**-
 * Diameter**-
 * Arc**-
 * Semicircle**-
 * Minor arc**-
 * Major arc**-
 * Central angle**-
 * Intercepted arc**-
 * Degree mesure of arcs**-

Section 2- Tangents to Circles
__**Objectives**__ Define tangents and secants of circles. Understand the relationship between tangents and certain radii of circles. Understand the geometry of radius perpendicular to the chord of a circle

__**Definitions**__ to a circle is a line that intersects the cirlce at two points. is a line in th eplane of the circle that intersects the circle at exactly one point, which is know as the point of tangency. if a line is tangent to a circle, then the line is perpendicular to the radius of the circle drawn at the point of tangency. A radius that is perpendicular to a chord of a circle bisects the chord. If a line is perpendicular to a radius of a circle at its endpoint on the circle, then the line is tangent to the circle. The perpendicular bisector of a chord passes through the center of the circle.
 * Secant**-
 * Tangent**-
 * Tangent theorem**-
 * Radius and Chord Theorem**-
 * Converse of Tangent theorem**-
 * Theorem**-

[|pic of circle with tangent at point of tangency(flickr.com)]



If the photo above had a radius of 10 and the part from tghe center of the circle to the chord is 6, then how long is is the chord? to get that you take 3² + 5² c² so then 9+ 2534. than you take the square root of that and get 5.830951895. take that number and double it and you will get 11.66190378. That is the lenght of the chord.

Heres a web site that will help you understand tangents and secants beter.[|Tan and sec web site] Srroll around and do the activities on the page.

Section 3- Inscribed Angles and Arcs
__**Objectives**__ Define inscribed angle and intercepted arc Delope and use the inscribed angle theorem and its corollaries.

__**Definitions**__ is an angle whose vertex lies on a chord and whose sides are chords of the circle. If an inscribed angle intercepts a semicricle, then the angle is a right angle. If two inscribed angles intercept the same arc, then they have the same measure.
 * Inscribed angle theorem-**
 * Right angle corollary**-
 * Arc-intercept corollary**-

Section 4- Angles Formed by Secants and Tangents
__**Objectives**__ > **__Definitions__** > **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 an angle formed by two secants that intersect in the exterior of a circle is the of the measures of the intercepted arcs. > **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. > ==Section 5- Segments of Tangents, Secants, and Chords== > **__Defintitions__**
 * Define angles formed by secants and tangents of circles.
 * Develope and use theorems about measures of arcs intercepted be these angles.
 * __Objectives__**
 * Define special cases of segments related to circles, including secant-secant, secant-tangent, and chors-chord segment
 * Develope and use theorems about measures of the segments

Section 6- Circles in the Coordinate Plane
1. Develope and use the equation of a circle. 2. Adjust the equation for a cricle to move the center in a coordinate plane.
 * __Objectives__**

__**Example**__ 1. Equation for a circle with a center at the origin is, x² + y² = r². r is the radius find the x and y intercepts

The intercepts are: (12,0), (-12,0) , (0,12) , (0,-12)

The equation is: x² + y² = 12²

[|web site for coordinate plane.]