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The value of yyy that minimizes the sum of the two distances from (3,5) (3,5)(3,5) to (1,y) (1,y) (1,y) and from (1,y) (1,y) (1,y) to (4,9) (4,9) (4,9) can be written as ab\frac{a}{b}ba where aaa and bbb are coprime positive integers. Find a+ba + ba+b.
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