Let ΔABC be a triangle with circumradius 5 and inradius 2 . Three (purple) circles with radius r are inscribed in angles ∠BAC, ∠CBA, ∠ACB, respectively such that the circles are in the interior of the triangle and there exists another circle (yellow) with radius r which is tangent to all three circles. Find r and round to 4 significant figures.
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