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http://argyll.epsb.ca/jreed/math9/strand3/3103.htm http://education.yahoo.com/homework_help/math_help/problem?id=minigeogt_9_1_1_10_80

__**CHORDS AND ARCS**__

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
 * Objectives:**



__Cirlce-__ A cirlce is the set of all points in a plane that are equidistant from a given point in the plane known as the center of teh circle. __Radius-__ A radius is a segment from the center of the circle to a point on the cirlce. __Chord-__ A chord is a segment whose endpoints line on a cirlce. __Diameter-__ A diameter is a chord that contains the center of a cirlce. __Central Angle-__ A central angle of a circle is an anle in the plane of a circle whose vertex is the center of the cirlce. __Intercepted Arc-__ 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 arc of the central angle. __Degree Measure of Minor Arc-__ The measure of its central angle. __Degree Measure of Major Arc-__ 360° minus the degree measure of its minor arc. __Degree Measure of Semicircle-__ 180° __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/360°(2‹pi›//r//)
 * Definitions:**

__Chords and Arcs Theorem__- In a circle, or in congruent circles, the arcs of congruent chords are congruent. __The Converse of the Chords and Arces Theorem-__ In a circle or in congruent circles, the chords of congurent arcs are equal.

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example:

Real World: One real world creation using the lesson of creating circles and arcs is the study of making contact lenses. In order for the contact to work out right, you will need to know the principles of a circle.

__**Tangents to Circles**

Define tangents and secants of cirlces Understand the relationship between tangents and certain redii of circles Understand the geometry of a radius perpendicular to a chord of a circle
 * Objectives**

__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 exactly one point. __Theorem__- The perpendicular bisector of a chord passes through the center of the circle. __Secant__- A line that intersects a circle at two points. __Tangent__- In a right triangle, the ratio of the length of the side opposite an aute angle to the length of the side adjacent to it. __Point of Tangency__- The point of intersection of a circle or sphere with a tangent line or plane.
 * Definitions**__

__Tangent Theorem__- If a line is tangent to a circle, then the line is perpendicular to a radius of the circle drawn to the point of tangency. __Radius and Chord Theorem__- A radius that is perpendicular to a chrod of a circle bisects the chord. __Concerse 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 tangent to the circle.

example:

__INSCRIBED ANGLES AND ARCS**__
 * [[image:err.JPG]]

Define inscribed angle and intercepted arc Develop and use the Inscribed Angle Theorem and its corollaries
 * Objectives:**

__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
 * Definitions:**

__Inscribed Angle Theorem__- The measure of an angle inscirbed in a circle is equal to half the measure of the intercepted arc

example:

__ANGLES FORMED BY SECANTS AND TANGENTS__**
 * [[image:94.JPG]]

Define angles formed by secants and tangents of circles Develop and use theorems about measures of arcs intercepted by these angles
 * Objectives:**

__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 is 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 with its vertex outside the circle is
 * Definitions:**

example:
 * __SEGMENTS OF TANGENTS, SECANTS, AND CHORDS__**

Define special cases of segmans relaed to circles, including sacant-secant, seant-tangent, and chord-chord segments Develop and use theorems about measures of the segments
 * Objectives:**

__Theorem__- If two segments are tangent to a circle from the same external point, the the segments ? __Theorem__- If two secants intersect outside a circle, the product of the lengths of one secant segment and its external segment equals ? (Whole x Outside = Whole x Outside) __Theorem__- If a secant and a tangent intersect outside a circle, then the product of the lenghts of the secant segment and its external segment equals ? (Whole x Outside = Tangent Squared) __Theorem__- IF two chords intersect inside a circle, then the porduct of the lengths of the segments of one chord equals ?
 * Definitions:**


 * __CIRCLES IN THE COORDINATE PLANE__**

Develop and use the equation of a circle Adjust the equation for a circle to move the center in a coordinate plane
 * Objectives:**