2021 Fall AMC 10A Problem 17

An architect is building a structure that will place vertical pillars at the vertices of regular hexagon ABCDEF, which is lying horizontally on the ground. The six pillars will hold up a flat solar panel that will not be parallel to the ground. The heights of pillars at A, B, and C are 12, 9, and 10 meters, respectively. What is the height, in meters, of the pillar at E?

\textbf{(A) }9 \qquad\textbf{(B) } 6\sqrt{3} \qquad\textbf{(C) } 8\sqrt{3} \qquad\textbf{(D) } 17 \qquad\textbf{(E) }12\sqrt{3}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.