Bicorne Graph

Inspired by a Tumblr link to this page from the curve encyclopedia. http://www.mathcurve.com/courbes2d/bicorne/bicorne.shtml A proper bicorne graph has tangents at the corners that pass through the vertex. Is the actual bicorne hat a mathematical bicorne? I don't understand the construction of the false bicorne on this page, though! I can't determine how the locus point is constructed.