A standard result in geometry is that the medians of a triangle meet at a point and cut each other[br]in the ratio of 2:1[br][br]Suppose we subdivide each leg of the triangle in two parts so that the ratio of the two parts is not 1:1 as in the case of medians, but rather n:1. Then we draw lines from the vertices to these points - let's call these lines [b][i]n-dians[/i][/b].[br][br]The three [i][b]n-dians[/b][/i] no longer intersect at a point - rather they define a triangle. What is the relationship between this triangle and the original triangle?[br][br]What can you say about the lengths of the segments determined by the intersections of the [i][b]n-dians[/b][/i]?[br][br]Can you prove {some, all} of your assertions?