Problem posed as challenge - Given a line segment as diagonal of a square construct square by using point, line segment, Point of Inter-section, and compass tools only.

Let A-C be the given diagonal.
Step -1 With A-C as radius and with centers as A & C respectively draw two circles.
Step - 2 Find the points of Intersection of these two circles. Line connecting these is perpendicular bisector of A-C.
Step - 3 with center as center point of A-C draw a circle passing through A & C. Find points of inter-section of this circle with perpendicular bisector of A -C. These are the vertices of square namely B & D
Step - 4 Complete the square A-B-C-D and hide all construction lines.
posted by Vasant Barve <vasantbarve@gmail.com>