Pasted

box% octave
GNU Octave, version 5.2.0
Copyright (C) 2020 John W. Eaton and others.
This is free software; see the source code for copying conditions.
There is ABSOLUTELY NO WARRANTY; not even for MERCHANTABILITY or
FITNESS FOR A PARTICULAR PURPOSE.  For details, type 'warranty'.
 Octave was configured for "x86_64-pc-linux-gnu".
 Additional information about Octave is available at https://www.octave.org.
 Please contribute if you find this software useful.
For more information, visit https://www.octave.org/get-involved.html
 Read https://www.octave.org/bugs.html to learn how to submit bug reports.
For information about changes from previous versions, type 'news'.
 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>