Abstract: We study Bernoulli first-passage percolation on the triangular lattice in which sites have 0 and 1

passage times with probability p and 1-p, respectively. At p=1/2, we obtain explicit limit theorems for the

point to point passage times. For the supercritical phase, we give exact asymptotics for the passage times

from the origin to the infinite cluster with 0-time sites, as p tending to 1/2. The proof uses conformal  loop

ensemble (6), the critical exponent for correlation length and Kesten’s scaling relations.