The Wikipedia article on Steiner constructions mentions it, but doesn't explain it, and the source linked is a book I don't have. This has come up in a practical project.
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Here's a solution for circles with different radius that doesn't require right angle measurement or parallel lines:
- Draw a tangent on the larger circle
- Draw two tangents on the smaller circle that intersect where the first tangent touches the larger circle
- Draw two tangents on the larger circle where the tangents from step 2 intersect the larger circle opposite to the first tangent
- Find the intersection of the tangents from the 3rd step. A line from this to where the first tangent touches the larger circle must go through the center of the two circles.
- Repeat the above with the first tangent intersecting on a different point on the larger circle. The intersection of the lines from the 4th step is the center of the circle.
Edit: visual aid
*removed externally hosted image*
Very cool, and thanks for the diagram!
That will work for me, I think, but drawing a tangent isn't a standard straightedge operation. If Wikipedia is to be believed there's still a "pure" solution to be found, just involving connecting intersection points.
