How to get the coordinates of a point if the coordinates of three other points and the distance from these points to the desired point are known?

Question

Mathematics

There is such a problem: there are three points on the plane, the coordinates of which are known. And there is a fourth point. Its coordinates are unknown, but the distance from the fourth point to each of the three points is known. Is it possible to get the coordinates of the fourth point from this data? Or at least an approximate radius? I would be grateful for a link to a lecture or a chapter of a textbook that talks about this

Answer 1

You just need to cross 3 circles on the plane. The "circle intersection formula" is googled, for example, this or this .
Cross any 2 circles and from the two resulting intersection points choose the one that lies on the third circle.

Answer 2

a system of 3 equations - the intersection of three spheres (point as the center of the sphere and distance as the radius of the sphere).