A firm has a branch store in each of the three cities \( A, B \) and \( C \). Stores in cities \...

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A firm has a branch store in each of the three cities \( A, B \) and \( C \). Stores in cities \( A \) and \( B \) are \( 320 \mathrm{~km} \) apart and in city \( C \) is \( 200 \mathrm{~km} \) from each of them. The firm wants to build a godown equidistant from stores in cities \( A \) and \( B \) and the sum of its distances from all the stores is least. Based on the above information answer the following questions:
If \( G A=G B=x \), then \( G C= \)
(a) \( 120+\sqrt{x^{2}-25600} \)
(b) \( 120-\sqrt{x^{2}-25600} \)
(c) \( x \)
(d) \( 120-x \)
Fig. \( 17.63 \)
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