Equation of a plane (7)

Problem. Write the equation of the plane passing the point H(1,1,1) and cut the coordinates axes Ox, Oy, Oz at A, B, C respectively so that H is centre of the circumscribed of the trianlge ABC.

This is my code.

restart:

with(geom3d):

with(LinearAlgebra):

A:=:

B:=:

C:=:

H:=:

f:=(x,y,z)->x/a + y/b +z/c-1:

solve([f(H[1],H[2],H[3]) = 0, Norm(H - A, 2) = Norm(H - B, 2), Norm(H - A, 2) = Norm(H - C, 2)],{a,b,c}): assign(%):

sort(Equation(plane(P,x/'a' + y/'b' +z/'c'  - 1 = 0,[x,y,z])));

This is my code. Please comment to me. Thank you.