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urp:circles [2021-10-17]
nerf_herder
urp:circles [2021-11-19] (current)
nerf_herder
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   * __chord__ has two endpoints on a circle   * __chord__ has two endpoints on a circle
   * __secant__ is a line that contains a chord, but extends beyond the 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   * __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   * __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+  * __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. In the image, P is center point of the circle, line C is a chord and line S is a secant.
  
-If two chords AB, CD intersect at P, then AP * PB = CP * PD+**intersecting chord theorem** - If two chords AB, CD intersect at P (not necessarily the center), then AP * PB = CP * PD
  
-**Inscribed/​interior angle** = 1/2 of intercepted arc +All inscribed angles going to the two same points on the circle (but from different vertices) have the same angle
-  all inscribed angles going to the two same points on the circle (but from different vertices) have the same angle +
-  angle of intersecting secants theorem:  +
-      angle formed by the secant intersection = (opposite arc - adjacent arc)/2+
  
-An angle outside the circle with two secants ​(or tangents) will have an angle that is 1/2 * (difference ​of the intercepted arcs)+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. ​ **coterminal angle** - the rest of the circle outside the angle. ​
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       2π - |angle|, or |angle| - 2π for the negative angle       2π - |angle|, or |angle| - 2π for the negative angle
  
- +**area of an arc** (from a central angle):
-**area of an arc**:+
   a = rad*r²/​2 ​ .... comes from a = πr² for full circle, and the    a = rad*r²/​2 ​ .... comes from a = πr² for full circle, and the 
                       proportion of a circle in the arc is rad/2π                       proportion of a circle in the arc is rad/2π
                       so a = (rad/​2π)*(πr²)                       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
 +   
 +-------
 Back to [[geometry]] or [[math]] page. Back to [[geometry]] or [[math]] page.
urp/circles.1634508162.txt.gz · Last modified: 2021-10-17 by nerf_herder