Triangle with concurrent parallel line segments

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A triangle with sides measuring 12, 8, and 6 has concurrent parallel line segments intersecting at a single point inside. The problem was solved using a system of equations, resulting in a line segment length of 16/3. However, there is a concern regarding the lack of restrictions on the lengths of the segments or the intersection point's position. Clarification is sought on whether additional constraints were omitted from the problem description. The discussion emphasizes the need for precise conditions to solve the problem using Euclidean geometry.
LittleWolf
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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?
 
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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?
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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