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.

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

Sources

• 1933: D.M.Y. Sommerville: Analytical Conics (3rd ed.) ... (previous) ... (next): Chapter $\text {III}$. The Circle: $15$. Angle of intersection of two circles