Given a circle, its center, and a point on the circle find inscribed square using only straightedge and compass.
The easy way is to draw a line through the two points to find another vertex of the square, then a perpendicular to this line through the center of the circle and find the two remaining vertices.
But (*) there's another solution using two circles to find "helper" points (I cheated for this solution).
Why does this solution work? What properties of circles, triangles, or squares are at play here?
(*) problem 1.7 of 'euclidea' app ( https://www.euclidea.xyz/ )
======== edit to add gif of the construction: https://makeagif.com/i/-F6Gdu