Are there more than four isosceles, right-angled, INSCRIBED triangles in an ellipse? By inscribed, I mean all three vertexes should lie ON the ellipse.
I am attaching a simplified picture that shows my count of four such triangle. Two of them form the only inscribed square of an ellipse in the middle. The other two would exist at each end.
Are there any proof or studies showing that these are the only four, or are there more?
*Edit: As Deepak pointed, when I said four, I was not careful. If you draw the diagonal line in the inscribed square the other way, you can also have two others.
To give you a better idea, I'm specifically wondering whether there are isosceles right angled inscribed triangles at different locations entirely, as is shown in my supplementary diagram that has a question mark.
Note that in that diagram, I'm using a FAKE isosceles triangle (the two sides are not actually of same lengths), as I cannot find a true isosceles triangle. But I'm wondering whether a real one exists that looks similar to what is drawn.
from Hot Weekly Questions - Mathematics Stack Exchange
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