sctr31

=__9-1__= __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. Central angle - angle in the plane of a circle whose vertex is the center of the circle. Intercepted arc - Whose other points lie in the interior of the angle. Degree measure of arcs - The degree of a minor arc is the measure of its central angle. The degree measure of a major arc is 360' minus the degree measure of its minor arc. The degree measure of a semicircle is 180'. Example 1 - Find the length (Q,R) of the arc on Thomas Jones Mural circle when (A,S) are 1.5 feet long http://www.arm.ac.uk/history/instruments/Jones-Mural-Circle-with-observor.jpg Solution - If 1.5 equals one arc and you need to find what 3 arcs would be you would multiply 1.5 by 3 which would equal 4.5 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,pi,r) =9-2= __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 about chords and their intercepted arcs.
 * 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.

__Definitions__ Secant - Line that intersects the circle at two points. Tangent - Line in the plane of the circle that intersects the circle at on point. Point of tangency - The one point ^ Theorem - The perpendicular bisector of a chord passes through the center of the circle. If (A,G) is 10 and (T,F) is 6.2, How long is (F,Q)? Solution - If the diameter (A,G) is 10 then the radius (T,L) is 5. (10 divided by 2 is 5) to find (F,Q) you have to divide the radius by 2. (5 divided by 2 = 2.5) =9-3= __Objective__
 * Define inscribed angle and intercepted arc.
 * Develop and use the inscribed angle theorem and its corollaries.

__Definitions__ Inscribed angle - An angle whose vertex lies on a circle and whose sides are chords of the cycle. 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. http://summit.k12.co.us/schools/shs/StaffWebPages/YankowsK/geometry/geoCh12_files/image070.jpg Example 1 - Find the measure of angle ACB, arch AB is 85' Angle ACB is inscribed in O and intercepts AB. By the inscribed Angle Theorem: m angle ACB 1/2 mAB1/2(85') = 42.5' =__9-4__= __Objectives__ Example - If a Kent drives his race car and cuts through the center of the 360 degree circled track from his starting point (F) across the track to (P) and gives an arc of 180 degrees takes a left and drives 20 degrees and cuts back through in a completely straight line what is the arc when he returns between the spot he is now (K) and (F) Solution - The arc would be the same 20 degrees =__9-5__= __Objectives__ http://images.google.com/imgres?imgurl=http://www.robertossluggos.com/images/pizza.jpg&imgrefurl=http://www.robertossluggos.com/&h=304&w=300&sz=12&hl=en&start=3&um=1&tbnid=wHZlQ3_LRF2doM:&tbnh=116&tbnw=114&prev=/images%3Fq%3Dpizza%26svnum%3D10%26um%3D1%26hl%3Den Example 1 - If (O,Q) equals 8 inches. What is (A,O) using the 9.5.1 theorem?Solution - If two segments are tangent to a circle from the same external point, then the segments are of equal length.
 * Define angles formed by sectants and tangents of circles.
 * Develope and use theorems about measure of arcs intercepted by these angles.
 * 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__=

=__Objectives__= = = =http://www.ccs.k12.in.us/chsteachers/MNesbitt/Notes1.1_files/image007.jpg= Example - Given: x² + y²100 Find the ordered pairs by making a graph, use a graphing calculator to verify your graph. When creating the graph of a new equation, you shold locate the intercepts. To find the x-intercept(s), find the value(s) of x when y100 Find the ordered pairs by making a graph, use a graphing calculator to verify your graph. When creating the graph of a new equation, you shold locate the intercepts. To find the x-intercept(s), find the value(s) of x when y0.( When a graph crosses the x-axis, y0.) X² + 0² = 100 X² = 100 X = (+ or -)10 So the graph has two intercepts,(10,0) and(-10,0). To find the y - intercept(s), find the value(s) of y when X = 0. 0² + y² = 100 y² = 100 y = (+ or -) 10 The graph has two y - intercepts, (0,10 and (0,-10). =**__Theorem Boxs__**= http://www.math.com/ http://www.webmath.com/
 * Develope and use the equation of a circle. Objectives
 * Adjust the equation for a circle to move the center in a coordinate plane.
 * 9.1.5 Chords and Arcs Theorem - In a circle, or in congruent circles, the arcs of congruent chords are **congruent**
 * 9.1.6 The Converse of the Chords and Arcs Theorem - In a circle or in congruent circles, the chords of congruent arcs are **congruent**
 * 9.2.2 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.
 * 9.2.3 Radius and Chord Theorem - A radius that is perpendicular to a chord of a circle **bisects** the chord.
 * 9.2.4 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.
 * 9.3.1 Inscribed Angle Theorem - The measure of an angle inscribed in a circle is equal to **one-half** the measure of the intercepted arc.
 * 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 **one-half** the measure of its intercepted arc.
 * 9.4.3 Theorem - 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.
 * 9.4.4 Theorem - 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
 * 9.4.5 Theorem - The measure 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'
 * 9.5.1 Theorem - If two segments are tangent to a circle from the same external point, then the segments are of equal length
 * 9.5.2 Theorem - If to secants intersect outside a circle, 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 )
 * 9.5.3 Theorem - 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 )
 * 9.5.4 Theorem - 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