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Published byMyrtle Wells Modified over 9 years ago
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Warm Up
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9.2 Introduction To Circles
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1. Radius _____ 2. chord _____ 3. diameter _____ 4. secant _____ 5. tangent _____ 6. circle _____ Let’s talk about circles! We will construct a circle with some rope and tape!
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Diameter Radius C = 2 r = d A = r 2 7in. Write the formula Plug in the numbers Give an answer with units Leave in terms of unless otherwise stated Find the circumference and area of this circle.
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Find the circumference and area of the circle Leave in terms of r=7in.
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Symbol for a circle Named with a letter P P C D An arc is made up of two points on a circle and all points of the circle needed to connect those two points by a single path. The red portion of the circle is called arc CD CDsymbol
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The measure of an arc is equivalent to the number of degrees it occupies. A complete circle has 360 degrees. The length of an arc is a fraction of a circle’s circumference, so it is expressed in linear units, such as feet, centimeters, or inches.
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x-axis y-axis A(6,0) B (0,-6) Find the measure and the length of AB. Since the arc is one fourth of the circle, its measure is (360), or 90. The arc’s length ( l ) can be expressed as a part of the circle’s circumference. l =C = d = 12 = 3 or 9.42 units
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A sector of a circle is a region bounded by two radii and an arc of the circle. The figure at the left shows sector CAT of A. T C A Find the area of the sector CAT. Since we know that CT has a measure of 90, we can calculate the area of the sector CAT as a fraction of the area of A Area of sector CAT = (area of A) = ( 6 2 ) = 9 u 2 or 28.27 u 2
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B C A A chord is a line segment joining two points on a circle. A diameter is a chord that passes through the center of the circle. An inscribed angle is an angle whose vertex is on a circle and whose sides are determined by two chords of the circle AB and AC are chords, and <BAC is an inscribed angle. <BAC is said to intercept BC. (An intercepted arc is an arc whose endpoints are on the sides of an angle and whose other points all lie within the angle. * Measure of the intercepted arc is double the measure of the inscribed angle
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http://www.mathwarehouse.com/g eometry/circle/inscribed- angle.html
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Reflection review: y x H (4,9) T(10,2) Reflect point H over the y-axis to H’. Then find the slope of HT and of TH’
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