Distance Between 4 Points in a Plane
Is there a general formula for the locus of a point whose sum of distances from 3 other points is fixed? - A question on QuoraI started thinking about this and realized that an ellipse is what you get with a string tied to two points, and a circle is what you get with a string tied to one point. If the circle and the ellipse intersect, then the sum of the distances from the intersection to each of the other three points is fixed. This isn't going to give you a general formula, but you can graph it on Desmos, which I did. And once I got the circle and graph drawn, I started embellishing it. I labeled the points and when I did I found they could be moved, even on this embedded graph. Go to the graph on Desmos and you can adjust the sizes of the ellipse and the circle as well. It's kind of fun to play with.
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