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this post was submitted on 25 Jan 2024
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math
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This might be what you want:
https://en.m.wikipedia.org/wiki/Poncelet%E2%80%93Steiner_theorem
Specifically this part:
Some straight-line constructions, you might or might not need a compass to locate properly in order to draw them. But as the tools are usually defined for these kinds of constructions, actually drawing the circle without a compass is not possible.
Well. If you can find the center of the inscribed circle and its tangent points on the triangle, that might be what OP wanted.