2005 AIME I Problem 14

Consider the points A(0,12), B(10,9), C(8,0), and D(-4,7). There is a unique square \mathcal{S} such that each of the four points is on a different side of \mathcal{S}. Let K be the area of \mathcal{S}. Find the remainder when 10 K is divided by 1000 .