Construction
We are given points A, B, and C, and wish to construct a circle centered at A with the same radius as BC (the first green circle).
- Draw a circle centered at A and passing through B and vice versa (the red circles). They will intersect at point D and form equilateral triangle ABD.
- Extend DB past B and find the intersection of DB and the circle BC, labeled E.
- Create a Circle centered at D and passing through E (the blue circle).
- Extend DA past A and find the Intersection of the DA and the circle DE, labeled F.
- Construct a circle centered at A and passing through F (the second green circle)
- Because E is on the circle BC, BE=BC.
- Because ADB is an equilateral triangle, DA=DB.
- Because E and F are on a circle around D, DE=DF.
- Therefore, AF=BE and AF=BC.
Read more about this topic: Compass Equivalence Theorem
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