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HMMT November 2015 H3

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Consider a 3×33 \times 3 grid of squares. A circle is inscribed in the lower left corner, the middle square of the top row, and the rightmost square of the middle row, and a circle OO with radius rr is drawn such that OO is externally tangent to each of the three inscribed circles. If the side length of each square is 1 , compute rr.

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{5 \sqrt{2}-3}{6}

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