The starting point is a pair of a circle \({\mathcal {D}}\) and ellipse \({\mathcal {E}}\) , which is within \({\mathcal {D}}\) , so that there is a triangle inscribed in \({\mathcal {D}}\) and circumscribed about \({\mathcal {E}}\) . According to the famous Poncelet porism, we know that there is an infinite family of such triangles, so we will call \(\{D,E\}\) a 3-Poncelet pair. Using isogonal conjugacy, we develop a geometric construction that produces new families of circles that also form a 3-Poncelet pair with \({\mathcal {E}}\) . In fact, any circle that is the locus of isogonal conjugates of a fixed point with respect to the family of Poncelet triangles of the original 3-Poncelet pair \(\{D,E\}\) serves as an outer circle in a new 3-Poncelet pair with the same inner conic \({\mathcal {E}}\) . In the process, two special pairs of circles emerge as guide marks.
