# Steiner Theorem Generalized
Let(A=[0,0], B=[1,0], C=[u1,u2], C1=[x1,x2], B1=[x3,x4], A1=[x5,x6]):
SteinerA := Theorem(
    [equidistance(A,C1,B,C1), sdistance(C1,A,B)-t*sdistance(A,B),
     equidistance(C,B1,A,B1), sdistance(B1,C,A)-t*sdistance(C,A),
     equidistance(B,A1,C,A1), sdistance(A1,B,C)-t*sdistance(B,C)], 
    concurrent(A,A1,B,B1,C,C1), [x1,x2,x3,x4,x5,x6]);
Remark(
`This is a generalization of Steiner's theorem, discovered by D. Wang in Jan`,
`1994. It is unclear whether the theorem is new.  It is the centroid theorem`,
`when t=0, the orthocenter theorem when t is infinity, and Steiner's theorem`,
`when t is half the square root of 3.`
): 
