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