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 ...