My problem is motivated by software like Geogebra. Suppose that we are allowed to use the following two tools only:
given any two points, we can construct a line passing through both of them
given any three non-collinear points, we can construct a circle passing through all of them.
I tried to use these two tools to do some simple geometric constructions, such as bisecting an angle or a line segment but failed to achieve anything. I wonder whether it is possible to do these.
Note: As mentioned in John Hughes's answer, I have to clarify my problem. The setting of the problem is just like that in the classical compass and straightedge problem, but with the compass replaced by a 'three-point-one-cirlce' instrument.