GeoGebra Exercise
Explore the dynamic construction. Try to make a similar construction yourself!
D.Kobal with GeoGebra
You might know the 'visualization' of an ellipse by 'paper folding'. At least it seems it is an ellipse. Proof? Think, think...!
Using sequences we can nicely visualize it...:
Circle (cut out of paper) with the centre O. Point F inside the circle. Fold the circle so that a point T on the edge coincides with the point F. 'The fold' is a perpendicular bisector of the segment TF. Repeat the folding for other points T on the edge...