DownJen08

//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.

**Circle**
- Set of all points that are equal distance form the center point

**Radius**
- A segment that goes from the center of the circle to a point in the circle

**Chord**
- A segment with endpoints line on a circle.

**Diamteter**
- A chord that contains nthe center of a circle

**Central Angle**
- of a circle is an angle in the plane of a circle whose vertex is the center of the circle. Intercepted Arc- angle whose other points lie in the interior angle Degree Measure of Arcs- Of a minor arc- is the measure of its central angle Of a major arc- is 360 degrees minus the degree measure of its minor arc. Of a semi-circle- 180 degrees

Arc Length L=M/360 degrees

[|More stuff about chords]

//Objectives-//

 * Define tangents and secants of circles.
 * Understand relationships between tangents and certain radii of circles.
 * Understand the geometry of a radius perpendicular to a chord of circle

Secant
- of a circle, is a line that inntersects teh circle at two points.

Tangent
- A line in the plane of the circle that intersects the circle at exactly one point, that is called the Point of Tangency.

Theorem
-The perpendicular bisector of a chord passes through the center of the circle

[|more information about Tangents]

//Objectives-//
-Define inscribed angle and intercepted arc. -Develop and use the Inscribed Angle Theorem and its corollaries.

Inscribed Angle
-An angle whose vertex lies n 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 angle.

Arc-Intercept Corollary
-If two inscribed angles intercept the same arc, then they have the same measure [|Site to help you and where picture is from]

**9.4 Angles Formed by Secants and Tangents [[image:http://farm1.static.flickr.com/210/488436140_8dd827bc72_m.jpg width="240" height="161" link="http://flickr.com/photos/manganite/488436140/"]]**
If a tangent and a secant intersect on a circle at the point of tangency, then the measure of the angle formed is one-half the measure of its intercepted arc. __**Theorem 9.4.2**__ The measure of an angle formed by two secants or chords that intersect in the interior of a circle is half the sum of the measures of the arcs intercepted by the angle. __**Theorem 9.4.3**__ The measure of an angle formed by two secants that intersect in the exterior of a circle is half the difference of the measures of the intercepted arcs. __**Theorem 9.4.4**__ The measure of a secant- tangent angle with its vertex outside the circle is half the difference of the measures of the intercepted arcs. __**Theorem 9.4.5**__ The measures of a tangent-tangent angle with its vertex outside the circle is half the difference of the measures of the intercepted arcs, or the measure of the major arc minus 180°.
 * __Theorem:__** If a tangent and a secant intersect on a circle at the point of tangency, then the measure of the angle formed is the measure of its intercepted arc.
 * __Theorem 9.4.1__**

[|math games]

**9.5 Segments of Tangents, Secants and Chords**
Tangent line to the cemetary. If two segments are tangent to a circle from the same external point, then the segments are equal length. __**Theorem 9.5.2**__ If two secants intersect outside a circle, then the product of the lengths of one secant segment and external segment equals the product of the lengths of the other secant segment and its external segment. __**Theorem 9.5.3**__ 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 the length of the tangent segment squared. __**Theorem 9.5.4**__ 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 9.5.1__**

= =

Create an equation to graph a circle on the origin.

 * Create an equation to graph a circle not on the origin.**