Octagons!

Geometry Level 3

The octagon P 1 P 2 P 3 P 4 P 5 P 6 P 7 P 8 P_1P_2P_3P_4P_5P_6P_7P_8 is inscribed in a circle, with the vertices around the circle in the given order. Given that the polygon P 1 P 3 P 5 P 7 P_1P_3P_5P_7 is a square of area 5 5 and the polygon P 2 P 4 P 6 P 8 P_2P_4P_6P_8 is a rectangle of area 4 4 , find the maximum possible area of the octagon.

4 2 4\sqrt{2} 3 5 3\sqrt{5} 3 7 3\sqrt{7} 3 2 3\sqrt{2} 3 6 3\sqrt{6} 3 3 3\sqrt{3}

Vishruth Bharath by Vishruth Bharath , 17, USA

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