When inverse vol is not ERC

Three assets with equal volatility and correlations $\rho_{12} = 0.8$, $\rho_{13} = \rho_{23} = 0$. (a) Show that inverse-volatility (here: equal) weights do not have equal risk contributions, and compute the risk shares. (b) Without solving numerically, argue which asset(s) ERC overweights relative to equal weights, and why. (c) Solve for the ERC weights exactly. (Hint: by symmetry $w_1 = w_2$.)