Thank you. I knew about Fermat point though. But one of the angles of the triangle exceeds 120, does it work then too? The main idea of Fermat point is to minimize the sum of the distances from the vertices to the point. When an angle exceeds 120, Fermat point becomes one of the vertices. But then the minimum angle becomes 0. We can construct the Fermat point outside the triangle when the angle exceeds 120. It violates the sum of distances to be minimum property, but does it satisfy the angle property?