If the algebraic sum of the perpendicular distances from the points `(3, 1), (-1, 2) and (1, 3)` to a variable line be zero, and `|(x^2+1, x+1, x+2), (2x+3, 3x+2, x+4), (x+4, 4x+3, 2x+5)|= mx^4 + nx^3 + px^2 + qx+r` be an identity in `x`, then the variable line always passes through the point (A) `(-r, m)` (B) `(-m, r)` (C) `(r, m)` (D) `(2r, m)`