The nine letters to the left of the middle position are \(\texttt{P, A, C, O, R, T, C, E, L}\). Checking each one, only \(\texttt{P, C, R, T, C, L}\) are consonants, six letters in all, so the remaining three, \(\texttt{A}\), \(\texttt{O}\), and \(\texttt{E}\), must be the vowels. This confirms the answer as \(\boxed{3}\).