I am currently starting to teach math to highschool kids who don't do well on their own, and I'm teaching a guy about notable points and lines of a triangle (incenter, centroid, circumcenter, perpendicular bisector, etc) and since we already finished with all the definitions and properties that he needs for his test, I want him to be able to solve problems related to it in case he faces them in the test.
I gave him an excercise about a basketball court with three backboards, in which he had to choose the optimal place to get as many points as possbile in each one without moving, and one about a triangular room in which a pool was going to be placed, and he had to figure out the maximum size possible for it.
Both of these examples seem a bit unlikely to happen in reality and after searching a bit I was unable to find practical uses for these tools.
Any sample excercise you can come up with will be much appreciated.