Kaylee's+Link+To+Chapter+9

//9.1 Chords and Arcs//
Radius- A segment that connects the center of a circle with a point on the circle; one-half the diameter of a circle. Chord- A segments whose endpoints lie on a circle. Diameter- A chord that passes through the center of a circle; twice the length of the radius of the circle. Centeral Angle- An angle formed by two rays originating from the center of a circle. Intercepted Arc- An arc whose endpoints lie on the sides of an inscribed angle. Degree Measure of arcs- The measure of a minor arc is the measure of its centeral angle. The degree measure of a major arc is 360° minus the degree measure of its centeral angle. Circle- The set of points in a plane that are equidistant from a given point known as the center of the circle. //__**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 π r) //__**EXAMPLE**__// Find the length of an arc if the degree measure is 45° and the radius is 7. L=M/360 (2 π r) L=45/360 (2 π (7)) L=45/360 (43.98) L=5.4975 In a circle, or in congruent circles, the arcs of congruent chords are congruent In a circle or in congruent circles, the chords of congruent arcs are congruent
 * //Definitions//**
 * __//Chords And Arcs Theorem//__**
 * //__The Converse Of The Chords And Arcs Theorem__//**

//9.2 Tangents to Circles//


//**Definitions**// Secant- A line that intersects a circle at two points. Tangent Segment- A segment that is contained by a line tangetn to a circle and has one of its endpoints on the circle. Point of Tangency- The point of intersection of a circle or sphere with a tangent line or plane __//**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 chord of a circle bisects the chord. Circle A has a radius of 10 in. Segment AE is 4 in. Segment BD is perpendicular to segment AC at point E. Find segment BD (DE)² + 4² = 10² DE² + 16 = 100 -16 -16 DE² = 84 DE = the square root of 84. __//**Converse 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__//**

//9.3 Inscribed Angles and Arcs//


//**Definitions**// Inscribed Angle- An angle whose vertex lies on the circle and whose sides are chords of the circle.

Angle ACB is an inscribed angle __//**Inscribed Angle Theorem**//__ The measure of an angle inscribed in a circle is equal to one-half 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 two inscribed angles intercept the same arc, then the have the same measure.

//**9.4 Angles Formed by Secants and Tangents**//
__//**Theorem 9.4.1**//__ 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 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 one-half the sum of the measures of the arcs intercepted by the angle and its vertical angle. __//**Theorem 9.4.3**//__ The measure of an angle formed by two secants that intersect in the exterior of a circle is one-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 one-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 one-half the difference of the measures of the intercepted arcs, or the measure of the major arc minus 180°

//**9.5 Segments of Tangents, Secants, and Chords**//
__//**Theorem 9.5.1**//__ If two segments are tangent to a circle from the same external point, then the segments are of equal length __//**Theorem 9.5.2**//__ If two secants intersect outside a circle, then the product of the lengths of one secant segment and its external segment equals the product of the lengths of the other secant segment and its external segment. (Whole x Outside = Whole x Outside) __//**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. (Whole x Outside = Tangent 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.

//**9.6 Circles in the Coordinate Plane**//
x² + y² = r² Center of the circle anywhere but (0,0) equation (x-h)² + (y-k)² = r²
 * //__Conjectures:__//**
 * Develop and use the equation of a circle
 * Adjust the equation for a circle to move the center in a coordinate plane
 * //__Center of the Circle is (0,0) equation__//**

__//**CHAPTER 9 LINKS**//__
[|inscribed angles] [|Chords and Arcs] [|Secants and Tangents] [|How to graph circles]