urp:circles

*chord*has two endpoints on a 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*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, 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.

**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

urp/circles.txt · Last modified: 2021-11-19 by nerf_herder