Problem
TxO Math Bowl 2024 - Individuals B - Problem 14
In acute \triangle ABC, let D, E, F lie on BC, CA, AB respectively such that DE \perp AC, EF \perp AB, and FD \perp BC. Let D', E', F' be the intersections of the circumcircle of \triangle DEF with BC, CA, AB respectively. If [AE'F] = 4[CD'E] = 9[BDF'] = 16, find the area of \triangle ABC.
Note: [ABC] denotes the area of ABC.
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