Mcar520

=Chapter 9=

Objectives
1. Define circle and associated parts and use them in constructions. 2. Define and use degree mesure of arcs. 3. Define and use the length measure of arcs. 4. Prove a theorem about chords and their intercepted arcs.

Definitons
Circle: A set of all points on a plane the are equal distance from the center. Radius: Line segment from center of the circle to a point on the circle. Diameter: Chord the includes the center of the circle. Central angle: An angle in the plane of the circle whose veretx is the center of the circle. Intercepted Arc: An arc whose endpoints lie on the sides of the angle whose other points lie in the center. Degree measure of arcs: The degree mesaure of a minor arc is it's central angle. The degree mesaure for a major arc is 360 minus it's minor arc. Length of the arc: To find the length of an arc take the measure of that arc and divide it by 360 degrees times 2 pi radis.

Theroms
1. In a circle or congruent cricles the arcs of the congruent chords are equal.

Objectives[[image:125871761_b4bec297ec.jpg link="http://www.flickr.com/photos/ilumb/125871761/"]]
1. Define tangents and circles. 2. Understand relationship between tangents and radii of circles. 3. Understand the math of a radius perpendicular to a chord in a circle.

Definitons
Secant: A line segment that intersects and circle at two diffrent points. Tangent: A line on the same plane as a circle that intersects the cricle and only one point. This point is know as the point of tangency.

Theroms
1. If a line is tangent to a cricle then the line is perpendicular to the circle at the point of tangency. 2. A radius that is perpendicular to a chord of a cricle bisects that chord. 3. If a line is perpendicular to a raidus of a circle, then that line is a tangent. 4. A perpendicular bisector of a circle passes through the center of the circle.

Objectives
1. Define inscribed angles and intercepted arcs. 2. Develop and use the inscribed angle theorem and it's corollaries.

Defintons
1. An angle whose vertex lies on a circle and it's sides are chords.

Theroms
1. The measure of an angle inscribed in a circle is equal to half the measure of the intercepted arc.

Collaries
1. If an inscribed angle intercepts a semicircle, then the angle is a right angle. 2. If two inscribed angles intercept the same arc, then the have the same measure.

Objectives
1. Define angles formed by angles and tangents of circles. 2. Develop and use theorems about measures of arcs intercepted by the those angles.

Theroms
1. If a tangent and a secant intersect a circle on the point of tangency, then the measure formed is half that of the intercepted arc. 2. The measure of an angle formed by two secants or chords on a point of tangency is on half the sum of the intercepted arc of its vertical angle. 3. The measure of an angle formed =Links= http://library.thinkquest.org/10030/13arcsandc.htm [|http://www.netsoc.tcd.ie/~jgilbert/maths_site/applets/circles/tangents_to_circles.html] http://www.mathwarehouse.com/geometry/circle/inscribed-angle.html