In square A-C-D-B with side S, C-E is tangent to the semicircle Q1 with diameter B-D. Q2 is the inscribed circle of A-C-E. The tangent to Q1 and Q2 meets the sides of the square at F and H and intersects C-E at G. Q3 is the inscribed circle of C-G-H. What is the ratio of the radii of circles Q2 and Q3?.
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