SEAMO 2027 - Paper F - SET 04 - Self-study Question 7

In triangle $ABC$, the cevians $AD,BE,CF$ meet at the interior point $P$, with $D\in BC$, $E\in CA$ and $F\in AB$, as shown. Suppose $AP=a$, $BP=b$, $CP=c$ and $DP=EP=FP=x$. Given $x=3$ and $a+b+c=20$, find $abc$.

Original source image, preserving the printed mathematical labels and any disclosed source discrepancy.