how can i explain the action of Peaucellier's cell? I don't know how to attach the picture so I will tell you what it is
an instrument for drawing the inverse of any locus. It is formed by four equal rods, hinged at the corners of a rhombus APBP' and two equal rods connecting two opposite corners A and B to a fixed pivot O. A pencil point is inserted at P' and a tracing point at P or vice versa.
should I prove side OP * side OP' = side (OA)^2 - side (P'A)^2? (if it is, then how?) I don't know how to explain the action of Peaucellier's cell.