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Ellipse from circle

one man 1290 Maple
September 19 2024
1

This is a task from one forum:  “Let's mark an arbitrary point on the circle. Let's draw a segment from this point, perpendicular to the diameter, and draw a circle, the center of which is at this point, and the radius is equal to this segment. Let's mark the intersection point of the segment connecting the intersection points of the circles with the perpendicular segment. Prove that the locus of all such points is an ellipse.”
I wanted to get a picture of a numerically animated "proof" using Maple tools.
МАTH_HЕLP_PLANET.mw
 And in fact, it turned out that AB=2AC, or AC=BC.
circle ellipse

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