The Ungerecht Family Tree

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====Circles====
{{ :urp:circles.jpg?400|}}
  * __chord__ has two endpoints on a circle
  * __secant__ is a line that contains a chord, but extends beyond the circle
  * __tangent__ is a line that touches a circle at one point (a secant with chord length of zero)
  * __Intercepted arc__ is the part of the circle contained within the two lines
  * __Central angle__ is angle of two lines from the center of the circle, it has the same degrees as the intercepted arc
  * __Inscribed/Interior angle__ has two points and the vertex all on the circle itself, it has 1/2 the degrees of the intercepted arc

In the image, P is center point of the circle, line C is a chord and line S is a secant.

**intersecting chord theorem** - If two chords AB, CD intersect at P (not necessarily the center), then AP * PB = CP * PD

All inscribed angles going to the two same points on the circle (but from different vertices) have the same angle. 

The **intersecting secants theorem**, for secants or tangents that intersect outside of the circle says the angle formed by the secant intersection = (opposite arc - adjacent arc)/2

**coterminal angle** - the rest of the circle outside the angle. 
  eg. angle of 30°, the coterminal is 330°
  in radians, use the absolute value.  
      2π - |angle|, or |angle| - 2π for the negative angle

**area of an arc** (from a central angle):
  a = rad*r²/2  .... comes from a = πr² for full circle, and the 
                      proportion of a circle in the arc is rad/2π
                      so a = (rad/2π)*(πr²)

**length of arc**, given length of chord and radius:
  d = 2*r*sin(a/2r) 
     a = length of arc, d = length of chord, r = radius
     
**circumcircle** - a circle that touches the vertices of an polygon
   circumcircle of a triangle - has the center at the point where the
      perpendicular bisectors of the triangle's sides meet. 
      (might be outside the triangle).
   To find the radius: https://mathworld.wolfram.com/Circumradius.html
   
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The Ungerecht Family Tree

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