With the result of this exercise we get two congruent conics c' and c'' with perpendicular axes, see figure 7.
These conics belong to the set of the circumscribed conics of the triangle ABC, which has the four centres A, B, C, D on the circumcircle u.

So we have discovered a new remarkable point D of the triangle ABC.

By creating the point D as an intersection point of the two conics CINDERELLA reports in an information console that D lies on the circumcircle u of the triangle ABC.

So CINDERELLA gives us a strong evidence, that our conjecture is true by a technique called "Randomized Theorem Checking".

Unfortunately this information console doesn't exist for HTML-pages.

In figure 7 we can discover more interesting facts, but here is no space to explain all of them.