Square
When constructing square ABED I started with circle A, and copied it three times to create circles B, E, and D. Circle A had the radius B and D, circle B had radius E and A, circle E had radius B and D, and circle D had radius A and E. Then, I created sides AB, BE, ED, and DA which are congruent because they're radii of the same congruent circles. I then proved that lines and AD and BE, and lines AB and DE are parallel by drawing the perpendicular bisectors FG and HK. Next, I created circle A' with radius H, and made point N. Then, I made circle N with radius H and circle H with radius N. This then proved that AD was perpendicular to AB and since one angle is a right angle then all the angles must be right angles. Since all sides are congruent and has four right angles, ABED is a square.