Angle of Intersection of Circles equals Angle between Radii

Theorem
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 equal to the angle between the radii to the point of intersection.

Proof
From Normal to Circle passes through Center, the straight line passing through the center of a circle is normal to that circle.

Hence the radii $CA$ and $C'A$ are perpendicular to the tangents to $\CC$ and $\CC'$ respectively.


 * Circles-angle-intersection.png

Thus, with reference to the above diagram, we have that:
 * $\angle FAC = \angle DAC'$

as both are right angles.

Hence:

Hence the result.