Let a circle 
lie inside another circle 
. From any point on 
, draw a tangent to 
and extend it to 
. From the point, draw another tangent, etc. For 
tangents, the result is called an 
-sided Poncelet transverse.
If, on the circle of circumscription there is one point of origin for which a four-sided Poncelet transverse is closed, then the four-sided transverse will also close for any other point of origin on the circle (Dörrie 1965).
