For reference here's a GPT-3 output for the sample question: Solution: Suppose the given set of n points is A = (a 1 , a 2 , …, a n ). Between any two points

For reference here's a GPT-3 output for the sample question: Solution: Suppose the given set of n points is A = (a 1 , a 2 , …, a n ). Between any two points we will draw a line segment connecting them, and let the distance from a 1 to the line segment be d(a 1 ,a 2 ) and d(a 1 ,a 3 ) be the distance from a 1 to the line segment connecting a 2 and a 3. Since any two of the points determine a line segment connecting them, there are n–2 segments connecting the n–1 points. Let L be the common perpendicular bisector of two of these segments. So, d(a 1 ,a 2 ) = d(a 1 , L) and d(a 1 ,a 3 ) = d(a 1 , L). Now, we consider the triangle formed by the points (a 1 , a 2 ) and (a 1 , a 3 ). If we are given the points a 1 , a 2 and a 3 , we can easily find the sides of the triangle. Since d(a 1 ,a 2 ) + d(a 1 ,a 3 ) = d(a 1 , L) + d(a 1 , L) = 2d(a 1 , L), the triangle formed is right angled and therefore non-degenerate. We can easily calculate the rational area of such a triangle and the side lengths. Let us consider the simplest case when n = 3. We have three points (a 1 , a 2 , a 3 ) such that each of a 1 , a 2 and a 3 are different. Therefore, we can form a triangle by connecting a 1 , a 2