hule517

chapter nine

~*~9.1~*~
__objectives__ -discover a circle and its associated parts, and use them in construction -use the degree measure of arces -use the lenght measureof arces -show a theorem about chords and their intercopled arces

__Things to know!__ circle- a closed plane curve consisting of all points at a given distance from a point within it called the center radius- a straight line extending from the center of a circle or sphere to the circumference or surface chord-the line segment between two points on a given curve diameter- a straight line passing through the center of a circle or sphere and meeting the circumference or surface at each end arc- any unbroken part of the circumference of a circle or other curved line endpoints- Either of two points marking the end of a line segment semi-circle- a half circle

minor arc- arc measuring less than 180 major arc- arc measuring more than 180 central angle- an angle formed at the center of a circle by two radii intercepted arc- arc whose endpoints lie on the sides of the angle and whose other oints lie in the interior of the angle degree meaure of arcs... minor arc- measure of its central angle major arc- 360 minus the degree measure semi circle- 180 degrees heres a good website to help you with these terms check it out! arc Lenght- L= m/360(2pir) radius(green line) diameter (the white dial) chord (red line) tangents(blue lines) secants( red line) and a right angle (red lines)
 * heres a really cool picture that shows examples of a....

http://www.mathematicshelpcentral.com/lecture_notes/college_geometry_folder/circles.htm

__theorems__ chords and arcs theorem- in a circle, or in congruent circles, the arcs of chords of congruent arcs are congruent converse of chords and arcs theorem- in a circle, or in congruent circles, the choreds of congruent arcs are congruent

example of finding arc length

~*~9.2~*~
__objectives__ - find out tangents and secants of circles -get to know the relationship between tangents and certain radii of circles -get to know the geometry of a radius perpendicular to a chord of a circle

__things to know!__ secant-an intersecting line, that intersects the circle twice tangent-a line or a plane that touches a curve or a surface at a point so that it is closer to the curve in the vicinity of the point than any other line or plane drawn through the point point of tangency- when a line intersects the circle at exactly one point

__theorems__ theorem- the perpendicular bisector of a chord passes through the center of the circle 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 converse of the tangent theorem- if a line is perpendicular to a radius of a circle at its endoint on the circle, then the line is tangent to the circle

examples of different types of lines and circles tangent

a good site to look at not only for 9.2 but for all chapters would be [|www.themathlab.com]

~*~9.3~*~
__objectives__ -find out what an inscribed angle is and what an intercepted arc -use the inscribed angle theorem and its corollaries.

__things to know!__ inscribed angle- an angle inside of a circle right-angle Corollary- when an inscribed angle intercepts a semicircle, then the angle is a right angle arc-interceptedcorollary- 2 inscribed angles intercept the same arc, then they have hte sae measure

__theorems__ inscribed angle theorem-the measure of an angle inscribed in a circle is equal to one half the measure of the intercepted arc

a good site for this chapter would be http://www.ies.co.jp/math/java/geo/enshukaku/enshukaku.html

~*~9.4~*~
theorem 1- If a tangent and a secant ( or a chord) interesect on a circle at the point 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 2- The measure of an angle formed by 2 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 3- The measure of an angle formed by 2 secants that intersect in the exterior of a circle is one-half the difference of the measures of the intercepted arcs theorem 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 5- The measure of a tangent-tangent angle with its vertec outside the cirlce is one-half the difference of the measures of the intercepted arcs, or the measure of the major arc minus 180 degrees.

heres a pretty sweet site! =] http://www.mathsrevision.net/gcse/pages.php?page=13

~*~9.5~*~
__objectives__ -find special cases of segments related to circles, including secant-secant, secant-tangent, and chord-chord segments -use theorems about measures of the segments

__theorems__ theorem 1- If 2 segments are tangent to a circle from the same external point, then the segments area of equal length theorem 2- If 2 secants intersect outside a circle, then the product of the lenghts of one secant segemnt and its external segment equals the product of the lengths of the other secant segments and its external segment, (whoel X outside = Whole X outside) theorem 3- If a secant and a tangents intersect outside a circle, then the product of the lengths of the secant segment and its external segment equals the lenght of the tangent segment squared. (whole X outside = Tangent squared) theorem 4- if 2 chords intersect inside a circle, then the product of the lengths of the segments of one chord equals the product of hte lenghts of the segments of the other chord

~*~9.6~*~
__objectives__ -use the equation of a circle -adjust the equation for a circle to move the center in a coordinate plane

__other good sites to look at....__ http://www.answers.com/topic/secant-secant-theorem-svg http://www.algebralab.org/lessons/lesson.aspx?file=Geometry_CircleSecantTangent.xml http://www.regentsprep.org/Regents/math/geometry/GP14/CircleSegments.htm all pictures are from [|www.flickr.com] and [|www.google.com] the definitions are from [|www.dictionary.com]