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Published byCarolyn Vickrey Modified over 2 years ago

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Circles Zach Laughman, Jesse Nelson, Brandon Wright, Samantha Huggins

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Key Words Radius- a straight line from the center to the circumference of a circle of sphere Diameter- the distance from one end of circle to another Circumference- the enclosing boundary of a circle -the distance around a circle Start Angle- The angle in a circle at which you start to determine the degree of another angle Center- the middle point of the circle

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Radius Start Angle Diameter Center

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Origin and Construction Origin: a slice parallel to the base of a cone (see figure) Construction: a circle is made up of points that are equidistance from the origin

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Standard Form (X-h)^2 + (Y-k)^2 = r^2 (0,0) (X-0)^2 + (Y-0)^2 = r^2

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Geometric/Algebraic Form X^2 + Y^2 + aX + bY + c = 0 Get this form into Standard Form by completing the square Complete the Square: 1) Get all X’s and Y’s on the left side 2) Get all constants on the right side 3) Take half of the middle number, square it, and add it to both sides (for X and Y) 4) Simplify

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Rotated Form When rotating a circle, the angle is the only part of the circle that changes Same circle, rotated angle 90 degrees 135 degrees

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Circle Relationships An angle outside of the circle can be used to help find an angle within the circle AxB = CxD A(A+E) = C(C+F) A B C D 4 6 10 3 E F 4(4+6) = 3(3+x) X 13.333

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Conic Form The conic form of a circle is formed when you intersect a double napped cone and a plane

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Degenerate Case The point as the radius approaches zero

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Eccentricity Says how round something is The eccentricity of a circle is zero

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Application Science and Engineering Radar systems, latitude/longitude, seismology (locating where an earthquake started)

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