Inspired by Justin Wong

Geometry Level 3

Consider a circle with radius 1 and center \(O\). Points \(A, B \) are on the circumference such that \( \angle AOB = \frac{ \pi}{3} \).

What is the radius of the largest circle that can be inscribed in sector \(AOB \)?


Inspiration - I misread a problem that Justin told me from his recent math competition. It used \( \frac{\pi}{6} \), which had ugly calculations. This had a much simpler solution.

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