Ellipses inscribed in convex quadrilaterals

Asked Sep 18 '22 at 16:48

Active Sep 19 '22 at 01:38

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Given any convex quadrilateral Q, is there at least one ellipse that is contained in Q and also touches all 4 sides of Q?

If the answer is "yes", then how does one find such an ellipse with maximum area?

edited Sep 19 '22 at 01:38

asked Sep 18 '22 at 16:48

Nandakumar R

1

The answer is yes. There is an infinite number of ellipses that can be inscribed in a given convex quadrilateral $ABCD$. And the minimum area of these ellipses is zero, as the ellipses turns into a line segment $AC$ or $BD$. So you want to be looking at the ellipse with the maximum possible area instead. – Hosam Hajeer Sep 18 '22 at 21:47
Thanks for pointing out this slip. Edited the question. – Nandakumar R Sep 19 '22 at 01:38
1

Please see another post here. – Ng Chung Tak Sep 19 '22 at 01:52
Thank you very much! – Nandakumar R Sep 19 '22 at 04:25

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