I have the following problem:
On a line $l$ on this line are the centers of two circles $C_1$ and $C_2$ . Circles $C_1$ and $C_2$ do not intersect and are not tangent to eachother. (but one could be completely inside the other)
How to construct the circle $C_3$ also with its center on line $l$ that cuts both $C_1$ and $C_2$ at right angles?
This construction is (a bit) described at https://en.wikipedia.org/wiki/Ultraparallel_theorem there the explanation is a bit to complex (because it wants to use specified hyperbolic motions) and is i think not complete.
I would like to learn a simplified straight edge and compass construction.