Cr+Br+5+25


 * __//Chapter 9//__**


 * __CH 9.1 Chords and Arcs__**


 * Define a circle and it's 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:__ Points on a plane that are all equidistant from a central point. __Radius:__ Segment that connects the center point with any on the circle. __Chord:__ Segment that has the end point on a circle. __Diameter:__ Chord that passes through the center of the circle. __Arc:__ Unbroken part of the circle. __Endpoints:__ The end point of a segment or line. __Semi-Circle:__ Arc of a circle thats endpoints are the endpoints of a diameter. __Minor Arc:__ An arc of a circle that is less than a semi-circle. __Major Arc:__ An arc of a circle that is more than a semi-circle. __Central Angle:__ An angle whose vertex is the center point of a circle, with rays pointing out. __Intercepted Arc:__ Arc thats end points are on an in scribed angle. __Degree Mesure Of Arcs:__ Minor arc - Measure of its central angle. Major arc - 360°-degree measure of its minor arc. Semicircle - 180°


 * Arc Length:** Length = Central angle/360*2πRadius
 * Chords and Arcs Theorems:** In a circle or in congruent circles, the arc of congruent chords are congruent.

What would this be? (the picture)

A nifty question site. [|Click Here]

__**Ch 9.2 Tangents to Circle.**__


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

__Secant:__ A line intersecting a circle at 2 places. __Tangent:__ A line touching a circle at 1 point. __Point Of Tangency__: Point where a tangent line touches a circle.


 * Tangent Theorem:** If a line is tangent to a circle, 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 chord of a circle bisects the chord.
 * Converse of Tangent Theorem:** If a line is perpendicular to the radius of a circle at its endpoint on the circle, then the line is tangent to the circle.




 * __Ch 9.3 Inscribed Angles and Arcs.__**


 * Define inscribed angle and intercepted arc.
 * Develop and use the inscribed angle theorem and its corollaries.

__Inscribed Angle:__ 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.
 * Right Angle Corollary:** If an inscribed angle intercepts a semicircle, then the angle is a right angle.
 * Arc-Intercepted Corollary:** If two inscribed angles intercepted the same arc, then they have the same measure.

You have an ice cream cone, you want to find the degree of the arc at the opening. the insied arc is 5. What is the measure of the opening?
 * __Ch 9.4 Angles Fomed by Secants and Tangents__**
 * Define angles formed by secants and tangents of circles.
 * develop and use theorems about measures of arcs intercepted by these angles.

//Case # 1-// Vertex is on the circle.

//Case # 2-// Vertex is inside the circle.

//Case # 3-// Vertex is outside the circle.


 * Theorem 1:** 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 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 and its vertical angle.
 * Theorem 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.

What is the angle on the clock if arc 11 2 is 25? __**Ch 9.5 Segments of tangents, secants, and chords**__.


 * Define special cases of segments elated to circles, including secant-secant, secant-tangent, and chord-chord segments.
 * Develop and use theorems about measures of the segments.

__Tangent Segment: Secant Segment: External Secant Segment:__


 * Theorem 1:** If two segments are tangent to a circle from the same external point, then the segments are of equal length.
 * Theorem 2:** If two secants intersect outside a circle, then the product of the lengths of one secant segment and it external segment equals the product of the lengths of the other secant segment and its external segment. Whole*Outside=(Whole*Outside)
 * Theorem 3:** If a secant and a tangent intersect outside a circle, then the product of the lengths of the segment and its external segment equals the length of the tangent segment squared. Whole*Outside=Tangent Squared
 * Theorem 4:** If two chords intersect inside a circle, then the product of the lengths of the segments of one chord equals the products of the segments of the other chord. (Part1)*(Part2)=Part1*Part2




 * __Ch 9.6 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.


 * Circle With the Center At Origin:** x²+y²=r²
 * Circle With the Center Not on Origin:** (x-h)²+(y-k)²=r²

Basically what the whole chapter is about. [|Click Here]