kijo61

chapter 9 9.1

=**Objectives**=


 * define a circle and its associated parts, and use them in construction.
 * define and use the degree measure of arcs
 * define and use the length measure of arcs
 * prove a theorem anout chords and their intercepted arcs

=**Definitions**=
 * Circle** – a circle is the set of all points in a plane
 * Radius** – a radius is a segment from the center off the circle to a point in a circle
 * [|Chord]** – a segment whose endpoints live on a circle
 * Diameter** – a chord that contains the center of a circle
 * [|Arc]** – an unbroken part of a circle
 * Endpoints** – two distinct points on a circle divide the circle into two arcs
 * Semi-circle** – an arc whose endpoints are endpoints of a diameter
 * [|Minor arc]** – an arc that is shorter than a semi-circle of that circle
 * [|Major arc (game)]** that is longer than a semi-circle of that circle
 * Central angle** – an angle in the plane of a circle whose vertex is the center of the circle
 * Intercepted arc** – endpoints lie on the sides of the angle and whose other points lie in the interior of the angle
 * Degree measure of arcs** – the degree measure of a minor arc is the measure of its central angle. Major arc is 360 degrees minus the degree measure of its minor arc. The measure of a semi-circle is 180 degrees.

9.2

=**Objectives**=
 * 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

=**Blue Boxes**=

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, which is known as the point of tangency. If a line is tangent to a circle, then the line is perpendicullar to the radius of the circle drawn to the point of tangency. A radius that is perpendicular to a chord of a circle is the chord if a line is perpendicular to a radius of a circle at its endpoint on the circle, then the line is parallel to the circle the perpendicular bisector of a chord passes through the center of the circle
 * Secants and Tangents**
 * Tangent Theorem**
 * Radius and Chord Theorem**
 * Converse of the Tangent Theorem**
 * Theorem**

=Objectives=
 * 9.3**

=Blue Box's= an angle whose vertex lies on a circle and whose sides are chords of the circle the measure of an angle in a circle is equal to half the measure of the intercepted arc if an inscribed angle intercepts a semicircle, then the angle is a right angles if two inscribed angles intercept the same arc, then they have the same measure
 * define inscribed angle and intercepted arc
 * develop and use the inscribed angle theorem and its corallaries
 * Inscribed Angle**
 * Inscribed Angle Theorem**
 * Right-Angle Corollary**
 * Arc-Intercept Corollary**

=Objectives=
 * 9.4**


 * define angles formed by secants and tangents of circles
 * develop and use theorems about measures of arcs intercepted by these angles.

=**Blue box's**=

9.4.1 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 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 measure of the arcs intercepted by the angle and its vertical anglee measures of the intercepted arcs. the measure of an angle formed by two secants that intersect in the exterior of a circle is 1/3 the sum of the intercepted arcs the measure of a secant-tangent angle with its vertex outside the circle is 1/2 the central angle The measure of a tangent-tangent angle with its vertex outside the circle is half the central angle
 * 9.4.2 Theorem**
 * 9.4.3 Theorem**
 * 9.4.4 Theorem**
 * 9.4.5 Theorem**

=Objectives= =Blue box's=
 * 9.5**
 * define special cases of segments related to circles, including secant-secant,secant-tangent, and chord-chord segments.
 * develop and use theorems about measures of the segements

if two segments are tangent to a circle from the same external point, then the segments intercept If two secants intersect outside a circle,the product ofthe lengths of one secant segment and its external segment equals the other secant if a secant and a tangent intersct outside a circle, then the product of the lengths of the secant segment and its external segment equals the other secant. if two chords intersect inside a circle, then the product of the lengths of the segment of one chord equals the length of the other chord.
 * 9.5.1 Theorem**
 * 9.5.2 Theorem**
 * 9.5.3 Theorem**
 * 9.5.4 Theorem**



9.6 FIND THE RADIUS AND CENTER: 1. x^2 + y^2 = 100 solution is: the center is 10 because sq. root 100 = 10 the center is (0,0) because
 * Objectives**
 * develop and use the equation of a circle
 * adjust the equation for a circle to move the center in a coordinate plane