it is naturally understood that circles and their arcs cannot be drawn without the compass
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.
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.