Circles Do Not Intersect, They Are External To Each Other, The Point Lies On The Line Connecting Their Centers

Steps

1. Draw a line g, that goes through the centres of the two circles and through the point E
2. Find the intersection of F
3. Find the midpoint between F and A and C and F
4. These midpoints G and I are the results

Steps

1. Choose a point C as the center for circular inversion. Choose the radius of the circle so that it passes through the center of circle a, to which point C belongs to.
2. Display circles a and b in the circular inversion around the new circle c, which will create line a' and circle b'.
3. Construct a line perpendicular to line a' which passes through point C. The new line will intersect with circle b' in two points. Construct two lines parallel to line a', s₁ and s₂ on the two intersections.
4. Display both line s₁ and s₂ back on circle c through circular inversion.
5. The two newly created circles, k₁ and k₂, are the solutions to the problem.