Let(A = [-x1,0], B = [x1,0], C = [x2,x3], O = [0,x4], D = [x5,x6], P = [x5,0],
    Q = [x7,x8], R = [x9,x10]):
SimsonA := 
Theorem([arbitrary(A,B,C), circumcenter(A,B,C,O), equidistance(O,A,O,D),
         perpfoot(D,P,A,B,P), perpfoot(D,Q,A,C,Q), perpfoot(D,R,B,C,R)],
         collinear(P,Q,R), [x4, x6, x7, x8, x9, x10]);

Remark(
`   The line containing the feet is known as the Simson line (or sometimes`, 
`just the simson) of the point with respect to the triangle. Robert Simson`,
`(1687-1768) made several contributions to both geometry and arithmetic ...`,
`The ``simson' was attributed to him because it seemed to be typical of his`,
`geometrical ideas. However, historians have searched through his works for`,
`it in vain. Actually it was discovered in 1797 by William Wallace.        `,
`                                                                           `,
`                                    --- H. S. M. Coxeter and S. L. Greitzer`,
`                                                / Geometry Revisited, p. 41`
):
