box% octave
GNU Octave, version 5.2.0
Copyright (C) 2020 John W. Eaton and others.
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Octave was configured for "x86_64-pc-linux-gnu".

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octave:1> A = [ 29.72  -14.892  53.778]; B = [ 33.422 -14.57   53.145]; C = [ 32.351 -16.136  54.869];
octave:2> M = C + ((2*[A-C; B-C]*[A-C; B-C]')\([A*A'-C*C'; B*B'-C*C']-2*[A-C; B-C]*C'))'*[A-C; B-C]
M =

   31.614  -14.897   53.631

octave:3> [norm(A-M) norm(B-M) norm(C-M)]
ans =

   1.9001   1.9001   1.9001

octave:4>