Find midpoint of interval with compass but without ruler
This is my first attempt to use geogebra.
To find midpoint of interval AB draw circles a, b, with center A and B with radius AB, find intersections C and D, draw circles c,d with center C and D and radius CA, find intersection E of circle a with circle d, draw circle e centered at E with radius EC. find its intersection F with circle c, draw circle a' centered in A with radius AF, find its instersection G with circle b, draw circle g centered at G with radius GB and find intersection H with segment AB. Illustrate with a circle centered at H with radius HA and with interval DC that H is indeed the midpoint.

Prove that H is indeed the midpoint between A and B