Are tangent points allowed in ruler and compass constructions?
In classical constructions with ruler and compass, a construction proceeds from point to point where the points are intersections of lines and circles, i.e., where the lines and the circles cross each other. Are the points where the lines and the circles touch each other rather than cross, allowed as well?
More specifically, if I have constructed two circles and I know that they touch at some point, can I proceed with the construction using this point?
I don't know how you got the problem you describe. I've never mentioned anything like that. I have mentioned two other problems earlier in the thread.
Problem A:
Problem B:
Emphasis is on "compass only". No straightedge, no straight lines, nil, nada, niet!
The question in the thread was NOT how to solve these problems. I've solved both of them. (Without drawing any straight lines.)
My initial solution used a point where two circles constructed on an intermediate step