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Inscribed square

For any isosceles triangle, there is a unique square with one side collinear with the base of the triangle and the opposite two corners on its sides. The Calabi triangle is a special isosceles triangle with the property that the other two inscribed squares, with sides collinear with the sides of the triangle,are of the same size as the base square. A much older theorem, preserved in the works of Hero of Alexandria,states that, for an isosceles triangle with base b {\displaystyle b} and height h {\displaystyle h}, the side length of the inscribed square on the base of the triangle is