Circles

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# Circles - PowerPoint PPT Presentation

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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## PowerPoint Slideshow about ' Circles' - sancha

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Presentation Transcript

### 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
• 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

Diameter

Start Angle

Center

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
• (X-h)^2 + (Y-k)^2 = r^2

(0,0)

• (X-0)^2 + (Y-0)^2 = r^2
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
• 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
• 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
• The conic form of a circle is formed when you intersect a double napped cone and a plane
Degenerate Case
• The point as the radius approaches zero
Eccentricity
• Says how round something is
• The eccentricity of a circle is zero
Application
• Science and Engineering
• Radar systems, latitude/longitude, seismology (locating where an earthquake started)