Let    P  2        P    2          denote the projective plane over a finite field   F q        F    q         . A pair of nonsingular conics   (A,B)     (  A  ,  B  )        in the plane is said to satisfy the Poncelet triangle condition if, considered as conics in              P    2    (      F   ‾     q    )       , they intersect transversally and there exists a triangle inscribed in   A     A        and circumscribed around   B     B       . It is shown in this article that a randomly chosen pair of conics satisfies the triangle condition with asymptotic probability   1/q     1  /  q       . We also make a conjecture based upon computer experimentation which predicts this probability for tetragons, pentagons and so on up to enneagons.
['Jaydeep Chipalkatti']
On the Poncelet triangle condition over finite fields