VTMO 2022 — Grade 8 — vtmo Question 9

$B$ lies on $AC$. Equilateral $ABD , BCE$ lie on the same side. $N$ on $BE$ has $NE : NB = 4 : 5$; $AN$ meets $BD , CE$ at $M , P$. $AB = 16 \,\mathrm{cm}$ and areas $AMB , ENP$ are equal. Find $BC$.