A Magical Length

Given n points A[1..n] in the 2-D plane, where i-th point has two attributes A[i].x and A[i].y representing x-coordinate and y-coordinate. Find 3 points A[i], A[j], A[k] (i, j, k are distinct) such that distance(A[i], A[j]) + distance(A[j], A[k]) + distance(A[k], A[i]) is minimized. Here distance(A[i], A[j]) means the Euclid Distance, which is equals to sqrt( (A[i].x - A[j].x)^2 + (A[i].y - A[j].