I have a project in 10th grade math. we are meant to find a point that is the closest distance to 3 points in a triangle. The purpose is to build a railway station that is closest to 3 landmarks. We have taken a brief look on special segments of triangles in class. (orthocenter, centroid, incenter, and circumcenter). How can I find the point closest to the three points in a triangle?
Thank you
Excuse my basic knowledge, I think what I mean by "closest" is the shortest average distance from the "railway station" to each of the "landmarks". The purpose of the project is to find the ideal position for the "railway" station. I'd appreciate it if you gave the best options you know of with a brief description that I can then research further. 🙂
Here is an image
http://i.stack.imgur.com/ye5fD.jpg
Best Answer
I think you are looking for Fermat point. Read this wiki page for more details https://en.wikipedia.org/wiki/Fermat_point