Question

Find the four coincident centers of the equilateral triangle and explain the Euler-line degeneracy.

$$\begin{gathered}A=(9,-13+12\sqrt{3})\ B=(-3,-13),\quad C=(21,-13)\end{gathered}$$

Accepted Answer

$$\begin{gathered}G=O=I=H=(9,-13+4\sqrt{3})\ 	ext{Euler line not unique}\end{gathered}$$

Answer

$$\begin{gathered}G=O=I=H=(9,-13+4\sqrt{3})\ 	ext{Euler line unique}\end{gathered}$$

Answer

$$\begin{gathered}G=O=I=H=(9,-13+12\sqrt{3})\ 	ext{Euler line not unique}\end{gathered}$$

Answer

$$\begin{gathered}G=O=I=H=(9,-13)\ 	ext{Euler line not unique}\end{gathered}$$

Practice: Triangle Centers - Equilateral Coincidence