  We study the site version of (independent) first-passage percolation on the
triangular lattice $\mathbb{T}$. Denote the passage time of the site $v$ in
$\mathbb{T}$ by $t(v)$, and assume that $P(t(v)=0)=P(t(v)=1)=1/2$. Denote by
$a_{0,n}$ the passage time from $\textbf{0}$ to $(n,0)$, and by $b_{0,n}$ the
passage time from $\textbf{0}$ to the halfplane $\{(x,y):x\geq n\}$. We prove
that there exists a constant $0<\mu<\infty$ such that as $n\rightarrow\infty$,
$a_{0,n}/\log n\rightarrow \mu$ in probability and $b_{0,n}/\log n\rightarrow
\mu/2$ almost surely. This result confirms a prediction of Kesten and Zhang
(Probab. Theory Relat. Fields \textbf{107}: 137--160, 1997). The proof relies
on the existence of the full scaling limit of critical site percolation on
$\mathbb{T}$, established by Camia and Newman.
