Prove Proncelet’s Theorem via Resultant
Natalya Weir, Brent Wessel

Abstract
In this paper we will prove Poncelet’s Theorem for triangles. To be specific, we consider two conics where one conic is in interior of the other. We prove the existence conditions for a triangle that is circumscribed about interior conic, and also inscribed in the exterior conic. Moreover, we show that if the conditions are satisfied, then there exist infinitely many such triangles. Our approach consists of tow steps: first, we give an explicit condition for a line through two points on the exterior conic to be tangent to interior; then we prove the existence of Poncelet’s triangles by using concept of resultant.

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