the problem:

Find the equation of the sphere that contains the points A = (2,4,4) , B= (4,2,0) , and C = (4,0,2), if its center lies on the plane y=x.

My attempt:

|AB|= sqroot(24)

|BC|= sqroot(8)

|AC|= sqroot(24)

from this i guessed that the center of the circle was point A, since points B and C were both equal distances away from them.

which gives me an r = sqroot(24)

Thus, the equation of the sphere is:

(x-2)^2 + (y-4)^2 + (z-4)^2 = 24

My problem is... the center (2,4,4) is not on the plane y=x

I'm confused. any help?