Usefulness of Euler line in triangles?

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The Euler line in triangles connects key concurrency points, including the intersections of perpendicular bisectors, medians, and altitudes, but not angle bisectors. While it presents interesting geometric properties, its practical applications in real life are limited. Many discussions suggest that the Euler line is primarily of theoretical interest rather than practical use. The consensus leans towards viewing it as an intriguing mathematical concept rather than a tool for real-world applications. Overall, the Euler line is more about exploration in geometry than functional utility.
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Is the Euler line in triangles USEFUL for anything in real life? This is the line which contains the concurrency points for the intersections of the triangle perpendicular bisectors, the medians, the altitudes, but not the angle bisectors. Interesting stuff, but are these points which occur on the Euler line useful in any applications?
 
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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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