On a Pointwise Construction of the Lemniscate

Extract

The writer of the following lines is aware of the possibility that the property discussed below is not a new discovery. He will, of course, be grateful to any reader who will provide him with bibliographical references.

It is well known-that the nine point circle of a triangle is tangent to the 4 contact (i.e. the inscribed and the escribed) circles. Given two tangent circles and we propose to find the locus of vertices of the triangles (Δ) which admit as their nine point circle and as one of their contact circles.