2021 WSMO Team Round Problems/Problem 9

Problem

In triangle $ABC,$ points $D$ and $E$ trisect side $BC$ such that $D$ is closer to $C$ than $E.$ If $\angle{CAD}=\angle{EAD},ED=3,$ and $[AEB]=6,$ then find $[ABC],$ where $[ABC]$ is the area of $ABC$ .

Proposed by pinkpig

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2021 WSMO Team Round Problems/Problem 9

Problem

Solution