C.a.R. > Applications > Difficult > Intersection with the Circle only
One can construct everything with the circle only. To see, how the intersection of two lines can be constructed, show the hidden objects with a right mouse click. You see a lot of circles that make the construction. It uses reflection at a circle.
Note that the reflection at a circle from inside to outside cannot be done with a finite given construction in all cases, but must be modified for each case, depending on the distance of the reflected point. This is clearly unavoidable, since a circle is a limited element, which cannot create points in an arbitrary distance using the same number of steps in each case.
Of course, this construction uses some macros to do the job.