MeJa522

=Chapter 9=

9.1 Chords and Arcs
Objectives: Definitions: Radius-A segment from the center of the circle to a point on the circle. Chord-Segment whose endpoints line on a circle. Diameter-A chord that contains the center of a circle. Arc-An unbroken part of a circle. Endpoints-Any two distinct points on a circle that divide the circle into to arcs. Semicircle-An arc whose endpoints are endpoints of a diameter. Minor arc-An arc that is shorter than a semicircle of that circle. Major arc-An arc that is longer than a semicircle of that circle. Central angle-An angle in the plane of a circle whose vertex is the center of the circle. Intercepted arc-An ar whose endpoints lie on the sides of the angle and whose other points lie in the interior of the angle.
 * 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.

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(2pier)



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

Definitions: Secant-A line that intersects the circle at two points. Tangent-A line in the plane of the circle that intersects the circle at exactly one point. Point of Tangency-The point that a tangent intersects.

The perpendicular bisector of a chord passes through the center of the circle.



9.3 Inscribed angles and Arcs
Objectives:
 * Define inscribed angle and intercepted arc.
 * Develop and use the inscribed andgle theorem and its corollaries.

Definitions: Inscribed angle-An 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 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 they have the same measure.

9.4 Angles formed by Secants and Tangents
Objectives: Definitions: Three Case- 1.Vertex is on the circle A)Secant and Tangent B)Two Secants 2. Vertex is inside the circle A)Two Secants 3. Vertex is outside the circle A)Two Tangents B)Two Secants C)Secant and Tangent 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.
 * Define angles formed by secants and tangents of circles.
 * Develop and use theorems about measures of arcs intercepted by these angles.

9.5 Segments of tangents, Secants and Chords
Objectives:
 * 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 segments.

9.6 Circles in the coordinate plane.
Objectives: -When center of the circle is on the origin (0,0) then X2+Y2=r2 -When The center of the circle is not on the origin then (x-h)2+(y-k)2=r2
 * Develop and use the equation of a circle.
 * Adjust the equation for a circle to move the center in a coordinate plane.