2025 Cayley Problem 6

In the diagram, point D is on side AB of \triangle ABC and points E and F are on BC. For some positive real number t, the area of \triangle DBE is t, the area of \triangle DEF is t, the area of \triangle DFC is 2t, and the area of \triangle DAC is 4t. If the area of \triangle DEC is 63, what is the area of \triangle ABC?

\textbf{(A)}\ 168\quad \textbf{(B)}\ 105\quad \textbf{(C)}\ 84\quad \textbf{(D)}\ 189\quad \textbf{(E)}\ 126

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Cayley contests here.