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urp:circles

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Circles

  • chord has two endpoints on a circle
  • secant is a line that contains a chord, but extends beyond the circle
  • Intercepted arc is the part of the circle contained within the two lines, it has 1/2 the degrees of 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

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

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)

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)

Back to geometry or math page.

urp/circles.1634508763.txt.gz · Last modified: 2021-10-17 by nerf_herder