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 * //__Chapter 9__//**

Circle: The set of all points in a plane that are equidistant from a given point in the plane known as the center of a circle. Radius: A segment from the center of a 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 Central Angle: 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.
 * 9.1 Chords and Arcs**



Degree Measure of Arcs: The degree measure of a minor arc is the measurement of its central angle. The degree measure of a major arc is 360 degrees minus the degree mesure of its minor arc. the degree measure of a semicircle is 180 degrees. Arc Length: If r is radius 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 x pi x r) Chords and Arcs Theorem: In a circle, or in congruent circles, the arcs of congruent chords are __?__.


 * 9.2 Tangents to Circles**

Secant: A line that intersects the circle at 2 points. Tangent : A line in the plane of the circle that intersects the circle at exactly one point, which is known as the point of tangency.



Tangent Theorem: If a line is Tangent to a circle, then the line is __?__ a radius of the circle. Radius and Chord Theorem: A radius is perpendicular to a chord of a circle __?__ the chord Converse of the Tangent Theorem: If a line is perpendicular to a radius of a circle at its endpoint on the circle, then th line is __?__ to the circle.


 * 9.3 Inscribed Angles and Arcs**

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-Intercept Corollary: If 2 inscribed angles intercept at the same arc, then they have the same measure.




 * 9.4 Angles Formed by Secants and Tangents**

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 2 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 2 secants that intersect inthe exterior of a circle is __?__ the __?__ of the measures of the intercepted arcs.




 * 9.5 Segments of Tangents, Secants, and Chords**

Theorem: If 2 segments are tangent to a circle from the same external point, then the segments __?__. Theorem: If 2 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 lengths of the secant segment and its external segment equals __?__. (Whole x Outside = Tangent Squared) Theorem: If 2 chords intersect inside a circle, then the product of the lengths of the segment of one chord equals __?__.
 * wiki space pic

9.6 Circles in the Coordinate Plane**

EX: x^2 + y^2 = 16 Sketch and describe graph by finding ordered pairs that satisfy the equation. Use a graphing calculator to verify your sketch. x^2 + y^2 = 16 x^2 = 0 y^2 = 0 Sq. rt. of 16 = 4 coordinates for center = (0,0) radius = 4 x intercepts = (4,0), (-4,0) y intercepts = (0,4), (0,-4) wiki space pic