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