The incircles of a Poncelt grid

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If a Poncelet polygon comes from two confocal conics there is a wealth of additional geometric relations coming from it.

Here you can see different structures related to this geometric situation and their various interrelations. You can switch them on and off by pressing the buttons.

• lines: the lines tangent to the inner Poncelet conic.
• points: the intersection points of these lines, These are the points of the Poncelet grid.
• conics: the conics of the Poncelet grid. All of them are confocal in that case.
• incircles: the lines form cells, each of them admits an incircle.
• centers: the centers of the incircles.
• bisectors: the centers of the incircles lie on lines. They are angle bisectors of the tangents to the inner Poncelet conic.
• tangents: the centers of the incircles also lie other tangets of points and conics of the Poncelet grid.