  We derive the exact critical couplings ($x^*, y_{\rm a}^*$), where $y_{\rm
a}^*/x^* = \sqrt{1+\sqrt2} = 1.533\ldots\,$, for the polymer adsorption
transition on the honeycomb lattice, along with the universal critical
exponents, from the Bethe Ansatz solution of the O($n$) loop model at the
special transition. Our result for the thermal scaling dimension, and thus the
crossover exponent $\phi=\frac{1}{2}$, is in agreement with an earlier result
based on conformal invariance arguments. Our result for the geometric scaling
dimensions confirms recent conjectures that they are given by $h_{\ell+1,3}$ in
the Kac formula.
