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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

Circles

Zach Laughman, Jesse Nelson, Brandon Wright, Samantha Huggins


Key words
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


Circles

Diameter

Radius

Start Angle

Center


Origin and construction
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


Standard form
Standard Form

  • (X-h)^2 + (Y-k)^2 = r^2

    (0,0)

  • (X-0)^2 + (Y-0)^2 = r^2


Geometric algebraic form
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


Rotated form
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


Circle relationships
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


Conic form
Conic Form

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


Degenerate case
Degenerate Case

  • The point as the radius approaches zero


Eccentricity
Eccentricity

  • Says how round something is

  • The eccentricity of a circle is zero


Application
Application

  • Science and Engineering

  • Radar systems, latitude/longitude, seismology (locating where an earthquake started)