The steady-state temperature distribution in a square plate ABCD is governed by the 2-dimensional Laplace equation. The side AB is kept at a temperature of $100^\circ$C and the other three sides are kept at a temperature of $0^\circ$C. Ignoring the effect of discontinuities at the corners, the steady-state temperature at the center of the plate is obtained as $T_0^\circ$C. Due to symmetry, the steady-state temperature at the center will be the same ($T_0^\circ$C) when any one side of the square is kept at a temperature of $100^\circ$C and the remaining three sides are kept at $0^\circ$C. Using the principle of superposition, find $T_0$ (rounded off to two decimal places).