Definition:Angle of Intersection of Circles

Definition
Let $\CC$ and $\CC'$ be circles whose centers are at $C$ and $C'$ respectively.

Let $\CC$ and $\CC'$ intersect at $A$ and $B$.

The angle of intersection of $\CC$ and $\CC'$ is the angle between the tangents at the point of intersection.


 * Circles-angle-intersection.png

Of the two angles formed by the tangents, the angle taken is between:
 * the half-line of one tangent that passes completely outside both circles

and:
 * the half-line of the other tangent that passes through the interior of one circle.

Also see

 * Two Circles have at most Two Points of Intersection


 * Angle of Intersection of Circles equals Angle between Radii
 * Angle of Intersection of Circles is Equal at Both Points