The Ungerecht Family Tree

• 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, for secants that intersect outside of the circle:

    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)

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