The circular points at infinity have the following (unnormalised) areals: x = a^2 (2a^2 - b^2 - c^2) - (c^2 - b^2)(c^2 - b^2 + delta) y = b^2 (2b^2 - c^2 - a^2) - (a^2 - c^2)(a^2 - c^2 + delta) z = c^2 (2c^2 - a^2 - b^2) - (b^2 - a^2)(b^2 - a^2 + delta) where delta = ± sqrt(a^4 + b^4 + c^4 - a^2 b^2 - b^2 c^2 - c^2 a^2) = ± sqrt((-a-b-c)(-a+b+c)(a-b+c)(a+b-c)) = ± 4i [ABC], where [ABC] is the area of the reference triangle. The sign choice for delta determines which of the two circular points is being specified. Sincerely, Adam P. Goucher