# 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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