Three Externally Tangent Circles With Same Size

Steps

Procedure

1. Create a circle tangent to the third circle at one of the common points of the two given circles.
2. Invert all given circles with respect to the newly created circle.
3. Proceed as in the problem "Parallel lines, both tangent to a circle."
4. Invert both solution circles with respect to the circle created in step one.

Steps

Procedure

1. Dilate the circles into points.
2. Connect the points with line segments.
3. Find the center of the resulting triangle using angle bisectors.
4. Construct the circumcircle of this triangle – this circle passes through all the points.
5. Dilate this circle by the radius of the original circles, both towards and away from the center.

Steps

1. Draw three lines i, g and h, each passing through the centre of one of the circles and the point of contact of the other two circles.
2. Denote the intersection of these three lines as S₁, and this point is the centre of the two circles sought.
3. Their radii are determined by the lengths of the segments S_1G and S_1F, where G and F are the intersections of the line i and the circle b(works with any circle and its intersecting line).