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This is a Korean CSAT mathematics multiple-choice problem. Solve it and put only the correct choice symbol, one of ①, ②, ③, ④, ⑤, inside \boxed{}.
Problem 14 In the right triangleABCshown in the figure, AB= 3, BC= 4, and∠B= π 2 . Let Dbe the point on segmentABthat dividesABinternally in the ratio 2 : 1, so that AD:DB= 2 : 1. LetEbe the point where the circle with centerAand radius ADmeets segmentAC, and letFbe the point, other thanD, where the lineABmeets this circle. On the arcEFof this circle, choose a pointGsuch that CG= 2 √ 6. LetHbe a point on the circle passing throughC,E, andGsuch that ∠HCG=∠BAC. Determine the length of segment GH. [4 points] 5 ① 6 √ 15 5 ② 38 √ 10 25 ③ 14 √ 3 5 ④ 32 √ 15 25 ⑤ 8 √ 10 5
\boxed{④}
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