Geometric Construction 9

Construct an animation demonstrating Poncelet's Porism for circles: If two circles are so related that a triangle can be inscribed to one and circumscribed to the other, then there are infinitely many such triangles can be so drawn.

Modify the above situation to the case when the word "circumscribe" also means the extension of the sides of the triangle circumscribing the circle.

Construct an animation showing: if two circles are so related that a quadrilateral can be inscribed to one and circumscribed to the other, then there are infinitely many such quadrilaterals can be so drawn.

Construct an animation showing: if two circles are so related that a quadrilateral can be inscribed to one and circumscribed to the other exteriorly, then there are infinitely many such quadrilaterals can be so drawn.

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Construct an animation demonstrating: If two ellipsess are so related that a triangle can be inscribed to one and circumscribed to the other, then there are infinitely many such triangles can be so drawn.

Construct an animation showing if there exists one inscribed triangle of a given circle tangent to a fixed given ellipse externally, then there are infinitely many inscribed triangles of the circle having the same property.

Construct an animation showing if there exists one inscribed triangle of a given circle tangent to a fixed given parabola, then there are infinitely many inscribed triangles of the circle having the same property.

Construct an animation demonstrating: If a circle and a parabola are so related that a triangle can be inscribed to one and circumscribed to the other, then there are infinitely many such triangles can be so drawn.

Construct an animation showing if there exists one inscribed quadrilateral of a given circle tangent to a fixed given parabola, then there are infinitely many inscribed quadrilaterals of the circle having the same property.

Construct an animation showing if there exists one inscribed triangle of a given ellipse tangent to a fixed given circle externally, then there are infinitely many inscribed triangles of the ellipse having the same property.

Construct an animation showing if there exists one inscribed "star" of a given ellipse tangent to a fixed ellipse, then there are infinitely many inscribed "stars" of the ellipse having the same property.