The vertices of a square sheet of paper are A, B, C, D. The sheet is folded in a way that the point D is mapped to the point D′ on the side BC. Let A′ be the image of A after the folding, and let E be the intersection point of AB and A′D′. Let r be the inradius of the triangle EBD′. Prove that r\equal{}A'E. geometryinradiusperimeterperpendicular bisectorgeometry proposed