Now for the final part I will be showing that the area of ABC to the ratio of the area of DEF is greater than or equal to four.
We know that it will be close at a significant triangle center so we experiment with the circumcenter, orthocenter, incenter, and centroid.
At the circumcenter (with the circumcircle drawn) we get:
At the incenter (with incircle drawn) we get
And at the orthocenter we get:
And find it is equal to four at the centroid.
