I was already studying about Poncelet porism but unfortunately I couldn't find any useful thing about this theorem for two intersecting circles. even I don't know if it is true for intersecting circles .
I draw some pictures using GeoGebra and I find out after some finite steps of drawing tangents ($n$) the last tangency point will be one of the meeting points of circles therefore ($n+1$)th and $n$th tangent would be coincident and then ($n+2$)th and ($n-2)$th tangent would be coincident and the process follows till the ($2n$)th tangent coincide the first one so it seems the theorem is also true for intersecting circles but I can't find any mathematical proof for it. I tried to prove it using inversion like when two circles lie entirely one within the other but it is not possible to find an inversion such that circles become concentric.
please let me know if it this theorem is also true for meeting circles and how can I prove it or recommend some sources or links for this beautiful theorem. thanks!
edit: I just download an essay here according to link if there are two circles satisfying the formula $d^2=R^2-2Rr$ where $R,r$ are radius of circles and $d$ is distance between their centers, then there are infinitely many triangles inscribed in one and circumscribed about the other circle. how can I prove it?
this link may also help.
please let us to consider and solve the last part first. thanks in advance