Le partage de Toño

Geometry Level pending

Toño shared his property among his four children. This is a hexagon whose sum of the lengths of two consecutive sides is always equal to \( 149m. \) The share of each child is a triangular plot with a pool is tangent to each side. The vertices of the hexagon are located on a circle whose radius is equal to the sum of the radius of the pools. What is the greatest length of a side of the hexagon, rounded to the nearest meter?

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