If a circle is drawn through A, B and D, then what is the diameter of the circle?

Points A(0,2), B(2,3), D(0,2) — with k=2, D coincides with A. Using the previous analysis where k = 2 makes ABD form a circle: actually we need a valid k. With k determined, computing the circumradius of triangle ABD and doubling gives the diameter. The official answer is 3√10.