Bisecting a line segment with compass only (no ruler)

Asked Mar 14 '13 at 09:24

Active Mar 14 '13 at 09:24

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We all know the construction for bisecting a line segment with compass and ruler

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However, I wondered if it's still possible to find the midpoint of the segment without use of the ruler, by just constructing circles? You can of course approximate the midpoint, and I see how the problem is equivalent to do a perpendicular projection of a point onto a line with only the compass, but I just don't get the construction. Maybe Thales' theorem, or am I missing something?

Thanks in advance

asked Mar 14 '13 at 09:24

Dario

1,977

Dammit, http://math.stackexchange.com/questions/227285/constructing-the-midpoint-of-a-segment-by-compass?rq=1 :) – Dario Mar 14 '13 at 09:30
1

The Mohr-Mascheroni theorem states that every construction with straightedge and compass can be done with compass only. See also this page and that one. – Martin Mar 14 '13 at 09:44

Bisecting a line segment with compass only (no ruler)

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