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urp:circles
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urp:circles [2021-10-17] nerf_herder |
urp:circles [2021-11-19] (current) nerf_herder |
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| * __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) | * __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, it has 1/2 the degrees of the intercepted arc | + | * __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 (not necessarily the center), 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 |
| 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. | ||
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| 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.1634509498.txt.gz · Last modified: 2021-10-17 by nerf_herder
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