Circumentre as not always the best location

This file is related to a question like Task 6 from the Resource Booklet from Workshop 6. When you have a triangle with an obtuse angle, the circumcentre will be outside the triangle and the sum of the distances |AD|+|BD|+|CD| is less than 3 times the radius of the circumcircle. The points A, B, C, and D can be moved.