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.

  • lemmyng@lemmy.ca
    ·
    3 months ago

    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*

    • CanadaPlus@lemmy.sdf.org
      ·
      3 months ago

      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.