A geometry problem by Hahn Lheem

Geometry Level 3

Two points are picked at random on the circumference of a circle with equation \(x^2+y^2=1\). The probability that the length of the chord connecting these two points is greater than \(\sqrt{2-\sqrt{2}}\) can be expressed as \(\dfrac{m}{n}\), where \(m\) and \(n\) are positive, coprime integers. Find \(m^3+n^3\).

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