Enter circle centers (x, y) and radii, then click Find Intersections.

The intersection of two circles is determined by their centers and radii. Two circles can have zero, one (tangent), two, or infinitely many (identical) intersection points. The theoretical solution uses the distance between centers (d) and the radii (R1, R2). The conditions: if d > R1 + R2, circles are separate with no intersection; if d < |R1 - R2|, one circle is inside the other with no intersection; if d = R1 + R2 or d = |R1 - R2|, circles are tangent with one intersection point; if |R1 - R2| < d < R1 + R2, two intersection points exist. The coordinates are computed using the chord line equation and the Pythagorean theorem. The intersection points lie on the radical axis (common chord) of the two circles. This calculator is useful in computational geometry, CAD, robotics (path planning), and collision detection.

1. Enter Circle 1 center (x1, y1) and radius (R1).
2. Enter Circle 2 center (x2, y2) and radius (R2).
3. Click Find Intersections to compute intersection points.
4. The result shows status: no intersection, tangent, or two points.
5. For two intersections, chord midpoint and distances are shown.
6. Click Reset to restore default example values.