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Geometry—Ch. 11 Review 1) A line which intersects a circle in two points is called a ________________. 2) A segment which has one endpoint at the center of a circle and the other endpoint on the circle is called a ______________. secant radius

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Geometry—Ch. 11 Review 3) A segment which has its endpoints on the circle is called a ______________. 4) A chord which passes through the center of a circle is called a ______________. diameter chord

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Geometry—Ch. 11 Review 5) What’s the difference between a secant and a tangent? How are they similar? A secant intersects the circle in two points, where a tangent only touches the circle once. Secants and tangents are similar in that they are both lines.

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Geometry—Ch. 11 Review A B C D E F (F is the center of the circle.) Find the measure of each arc: 6) CD 31 79 101 70 CD + 31 = 101

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Geometry—Ch. 11 Review A B C D E F (F is the center of the circle.) Find the measure of each arc: 31 79 101 70 7) DEB8) AED = 79+101+79 = 259 = 180 AED is a semicircle!!!

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Geometry—Ch. 11 Review 9) Find the measure of arc ABC: A C B 77 154 206 77 * 2 = 154 360 – 154 = 206

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Geometry—Ch. 11 Review 10) Find the measure of arc TY: T O Y 93 122 B Since vertical angles are congruent, we have another 93 degree angle here. 93 Angle Y is an inscribed angle, so its measure is ½ the measure of arc OB. 61 The angles of a triangle add up to 180, so the missing angle here is 26 degrees. 26 Angle O is also an inscribed angle, so its measure is ½ the measure of arc TY. 52

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Geometry—Ch. 11 Review 11) Solve for x:. x 159 126 Since all circles contain 360 degrees, the missing arc is 75 degrees. 75 ½ (large arc – small arc) x = ½ (159 – 75) x = x = 42

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Geometry—Ch. 11 Review 12) Solve for x:. x 114 106 ½ (large arc + small arc) x = ½ (114 + 106) x = x = 110

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Geometry—Ch. 11 Review 13) Solve for x:. 28 89 x 171 We’ll temporarily call this arc “y”. y ½ (89 – y) = 28 89 – y = 56 y = 33 x + 33 + 89 + 171 = 360 x + 293 = 360 x = 67

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Geometry—Ch. 11 Review 14) Solve for x:. 8 x 22 15 (x)(15) = (8)(22) 15x = 176 x = 11.73

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Geometry—Ch. 11 Review 15) Solve for x:. x 3 13 4 (4)(4+x) = (3)(3+13) (outside piece)(entire segment) = (outside piece)(entire segment) 16+4x = 48 4x = 32 x = 8

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Geometry—Ch. 11 Review 16) Graph the following circle: (x-3) 2 + (y+2) 2 = 9 The center will be at (3,-2). …and the radius is 3 units long.

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17) Find the length of the arc from A to B: A B 78 o 5 cm Arc length = 2 r (angle/360) = 2 (approximately 6.81 square cm) Geometry—Ch. 11 Review

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