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Circles

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

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Circles

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

  2. 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

  3. Diameter Radius Start Angle Center

  4. 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

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

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

  7. 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

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

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

  10. Degenerate Case • The point as the radius approaches zero

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

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

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