Let a circle C_1 lie inside another circle C_2. From any point on C_2, draw a tangent to C_1 and extend it to C_2. From the point, draw another tangent, etc. For n tangents, the result is called an n-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.
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