Let $[ABCD]$ be a quadrilateral, $P=AC\cap BD$ and $h_A, h_C$ be the altitudes from $A$ and $C$ to $BD$, respectively. Moreover, let $p,q,r,s$ be the areas of $[ABP], [BCP], [CDP]$ and $[DAP]$, respectively. Then, $\frac{q}{r}=\frac{BP\times h_C/2}{DP\times h_C/2}=\frac{BP}{DP}=\frac{BP\times h_A/2}{DP\times h_A/2}=\frac{p}{s}\Rightarrow qs=pr$,which is absurd, since $p,q,r,s$ are distinct primes.