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Two sets of tangential, colored squares are positioned symmetrically in two identical regular octagons, as shown above.

Let \(f : (0,1) \to [0,1]\) be bijective.

Can \(f\) be continuous?

Is there a circle in the Cartesian plane which passes through exactly 4 points with rational coordinates?

A convex cyclic quadrilateral has side lengths \(a, b, c, d\). If the circumcircle has radius \(1\) and \[a\times b\times c\times d=4,\] then what is the ...

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