Porism

1. Illustrate Poncelet Porism: 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.
   
   

2. 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.
   
   

3. Given a circle with radius and a point
   
   construct a point on so The point B is called the inverse of with respect to the circle.
   
   

   1. Investigate the inversion of a straight line.

   2. Investigate the inversion of a circle.

4. Construct a script which constructs the inversion of a circle given its center and a point on the circumference.

5. Construct an animation making the chain of circles move about the center.
   
   

6. Construct an animation illustrating Steiner's Porism: For any two (nonconcentric) circles one inside another, if circles are drawn successively touching them and one another so the last one touches the first, then it will always happen whatever the position of the first circle.
   
   

7. Construct an animation illustrating Poncelet Porism for the case of two ellipses.