Let A(1,-1,-1), B(2,1,2), C(1, 3, 1) be three points and Delta: x = -t, y = -t, z = t be a line. Write the equation of the sphere (S), knowing that center of (S) lies on the line Delta, (S) passing the point A and cuts the plane passing through the three points A, B, C cut (S) a circle has least radius.

This is my code.

**> restart;**

**with(geom3d):**

**a:=[-t,-t,t]:**

**point(T,a):**

**point(A,1,-1,-1):**

**point(B,2,1,2):**

**point(C,1,3,1):**

**plane(ABC,[A,B,C],[x,y,z]):**

**d:=distance(T,ABC):**

**R:=distance(T,A):**

**r:=R^2-d^2;**

**sol:=minimize(r,'location');**

**coordinates(point(T1,op(eval(a,op(1,sol[2][1]))))):**

**rad:=subs(op(1,sol[2][1]),R):**

**Equation(sphere(S,[T1,rad],[x,y,z])):**

**Student[Precalculus][CompleteSquare](Equation(S));**

Please help me some following questions:

1) I can't use the commant expand(r) or simplify(r).

2) How i can use the commant in the line Student[Precalculus][CompleteSquare](Equation(S));?

3) Please comment to me at the line **coordinates(point(T1,op(eval(a,op(1,sol[2][1]))))):**

Thank you very much.