chvi624+Ch+9+link

=Chapter 9=

9.1 CHORDS & ARCS
OBJECTIVES- __Define a circle and its associated parts, and use them in constructions.__

OBJECTIVES- __Define and use the degree measure of arcs.__

OBJECTIVES- __Define and use the length measure of arcs.__

OBJECTIVES- __Prove a theory about chords and their intercepted arcs.__


 * __Definitions:[[image:arch_bridg_dddddddddddddd.jpg width="406" height="356" align="right" link="http://www.flickr.com/photos/jasperpg/404155802/"]]__**


 * CIRCLE-** __A set of all points in a plane that are equidistant from a given point in a plane known as the center of the circle.__


 * RADIUS-** __A segment frem the center of the circle to a point on the circle.__


 * CHORD-** __A segment whose endpoints line on a circle.__


 * DIAMETER-** __A chord that contains the center of a circle.__


 * ARC-** __An unbroken part of a circle.__


 * ENDPOINTS-** __Any two distinct points on a circle divide the circle into two arcs.__


 * SEMI-CIRCLE-** __An arc whose endpoints are endpoints of the diameter.__


 * MINOR ARC-** __A circle is an arc that is shorter than a semicircle.__


 * MAJOR ARC-** __A circle is an arc that is longer than a semi-circle of that circle.__


 * CENTRAL ANGLE-** __A circle is an angle in the plane of a circle whose vertex is the center of the circle.__


 * INTERCEPTED ARC-** __An arc whose endpoints lie on the sides of the angle and whose other points lie in the interior of the angle.__

**BLUE BOXES**

 * __DEFINITION OF A CIRCLE__**

A circle is the set of all points in a plane that are equidistant from a given point in the plane know as the center of the circle. A radius (plural, radii) ia s segment from the center of the circle to a point on the circle. A chord is a segment whose endpoints line on a circle. A diameter is a chord that contains the center of a circle.


 * __CENTRAL ANGLE AND INTERCEPT ARC[[image:pizzadddddddddddddddddddddddddddddd.jpg width="273" height="220" align="right" link="http://www.flickr.com/photos/49405310@N00/106074883/"]]__**

A central angle of a circle is an angle in the plane of a circle whose vertex is the center of the circle. An arc whose endpoints lie on the sides of the angle and whose other points lie in the interior of the angle is the intercepted ars of the central angle.


 * __DEGREE MEASURE OF ARCS__**

The degree measire of a minor arc is the measire of its central angle. The degree measure of a major arc is 360 degrees minus the degree measure of its minor arc. The degree measire of a semi-circle is 180 degrees.


 * __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 givenby the following: L= M/360 (2*pi*r)


 * __CHORDS AND ARCS THEOREM__**

In a circle, or in congruent circles, the arcs of congruent chords are congruent.


 * __EXAMPLE__**

Arc Length: The angle of the two lines is the measure of the arc.

**9.2 TANGENTS TO CIRCLES**
OBJECTIVES- Define tangents and secants of circles. OBJECTIVES- Understand the relashionship between tangents and certian radii of circles. OBJECTIVES- Understand the geometry of a radius perpendicular to a chord of cirlce


 * DEFINITIONS:[[image:379087208_56bd744a63.jpg width="380" height="342" align="right" link="http://www.flickr.com/photos/asmundur/379087208/"]]**


 * SECANT-** __A line that intersects at two points.__


 * TANGENT-** __A line in the plane of the circle that intersects the circle at exactly one point.__


 * POINT OF TANGENCY-** __The point of where the tangent line intersects with the circle.__

BLUE BOXES
__**SECANTS AND TANGENTS**__

A secant to a circle is a line that intersects the circle at two points. A tangent is a line in the plane of the circle that intersects the circle at exactlly one point, which is known as the point of tangency.


 * __TANGENT THEOREM__**

If a line is tangent to a circle, then the line is parallel to a radius of the circle drawn to the point of tangency.


 * __RADIUS AND CHORD THEOREM__**

A radius that is perpendicular to a cord of a circle intersects the chord.


 * __CONVERSE OF THE TANGENT THEOREM__**

If a lin is perpendicular to a radius of a circle at its endpoint on the circle, then the line is tangent to the circle.


 * __THEOREM__**

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


 * __EXAMPLE__**[[image:WIKI.JPG width="598" height="344"]]

9.3 INSCRIBED ANGLES AND ARCS
OBJECTIVES- Define inscribed angle and intercepted arc. OBJECTIVES- Develope and use the inscribed angle theorem and its corollaries.


 * DEFINITIONS:[[image:ghjfgdfjfgyighjkfghjfdthjmvghjty.jpg align="right" link="http://www.flickr.com/photos/45688285@N00/6050999/"]]**


 * INSCRIBED ANGLE-** __An angle whose vertex lies on a circle and whose sides are chords of the circle.__

BLUE BOXES

 * __INSCRIBED ANGLE THEOREM__**

The measure of an angle inscribed in a circle is equal to twice the measire of the intercepted arc.


 * __RIGHT-ANGLE COROLLARY__**

If an inscribed angle intersepts a semi-circle, then the angle is a right angle.


 * __ARC-INTERCEPT COROLLARY__**

If two inscribed angles intercept the same arc, then they have the same measure.


 * __EXAMPLE__**

If there is an inscribed angle, the angle is one half of the arc connected. i.e. The angle is 13 degrees, then you have to double that number to get the measure of the arc, which would equal 26 degrees.

**9.4 ANGLES FORMED BY SECANTS AND TANGENTS**
OBJECTIVES- define angles formed by secants and tangents of circles.

OBJECTIVES- develope and use theorems about measures of arcs intercepted by these angles.


 * DEFINITIONS:[[image:aaaaaaaaaaaaaaaaaaaaaaaaaaaaaa.jpg width="304" height="298" align="right" link="http://www.flickr.com/photos/22385015@N00/299742228/"]]**

None.


 * CLASSIFICATION OF ANGLES WITH CIRCLES:**

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 * 1.** Vertex is on the circle. 2. Vertex is inside the circle.

BLUE BOXES

 * __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 half the measure of its intercepted arc.

__**Theorem**__

The measure of an angle formed by two secants or chords that intersent in the interior of a circle is half the sum of the measures of the arcs intercepted by the angle and its vertical angle.


 * __Theorem__**

The measire of an angle formed by two secants that intersect in the exterior of a circle is the of the measure of the intersepted 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

**9.5 Segments of Tangents, Secants, and Chords**
OBJECTIVES- Define special cases of segments related to circles, including secant-secant, secant-tangent, and chord-chord segments.

OBJECTIVES- Develope and use theorems about measures of the segments.


 * DEFINITIONS:** None[[image:SEGMENTS_VBGHJMNVGHJBGVsdfghjkllkkkkkkk.JPG width="315" height="245" align="right"]]

BLUE BOXES

 * __Theorem__**

If two segments are tangent to a circle from the same external point, then the segments intercept.


 * __Theorem__**

If two secants intersect outside a circle, the product of the lengths of one secant segment and its external segment equals the other secant.


 * __Theorem__**

If a secant and a tanent intersect outside a circle, then the product of the lengths of the secant segment and its external segment equals the other secant**.

__Theorem__**

If two chords intersect inside a circle, then the product of the lengths of the segments of one chord equals the length of the other chord.

9.6 Circles in the Coordinate Plane
OBJECTIVE- Develope and use the equation of a circle. OBJECTIVE- Adjust the equation for a circle to move the center in a coordinate plane.


 * DEFENITIONS:** none

BLUE BOXES-
none


 * __Example__**

(x^2+2)+(y^2-3)=25 The x and the y are the center of the of your circle.

The =25 is your radius squared.

It would look like this.

__HERE ARE SOME FUN AND USEFUL LINKS.354__

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