Triangle with concurrent parallel line segments

[LittleWolf]

I was asked to solve the following problem. A triangle has sides of length 12,8 and 6. There are line segments of equal length that are parallel to each side of the triangle and intersect at one point(concurrent) inside the triangle, what is the length of line segment? I solved the problem by setting up a system of equations. The length of the line segments turned out to be 16/3. Does anyone know how to solve this problem using euclidean geometry?

 

[uart]

You know that unless you place some other restriction (for example that the ends of the line segments must lay on the sides of the triangle for example) then there is no restriction to either the lengths of the line segments or to the position of their intersection point. Are you sure you haven't left something out of the problem description?