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A square $ABCD$ has side 40 units. Point $F$ is the midpoint of side $AD$. Point $G$ lies on $CF$ such that $3CG = 2GF$. What is the area of triangle $BCG$?

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Source: UK Mathematics Trust, licensed © UK Mathematics Trust; past papers published free at ukmt.org.uk. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project. Solutions are the publisher's, linked not copied.