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Dhoni starts from his office at $ 8 $ A. M. on a Sunday morning, travels $ 10 $ km towards West and then turns to his left and walks $ 8 $ km. Then he again turns to his left and walks $ 4 $ km and then stops. What is the shortest distance to his office from the point where he stopped?
All the roads of a city are either perpendicular or parallel to one another. The roads are all straight. Roads $ A, B, C, D $ and $ E $ are parallel to one another. Roads $ F, G, H, I, J, K, L $ and $ M $ are parallel to one another.
Road $ A $ is $ 1\text{ km} $ East of road $ B $ .
Road $ B $ is $ 1/2\text{ km} $ West of road $ C $ .
Road $ D $ is $ 1\text{ km} $ West of road $ E $ .
Road $ G $ is $ 1/2\text{ km} $ South of road $ H $ .
Road $ I $ is $ 1\text{ km} $ North of road $ J $ .
Road $ K $ is $ 1/2\text{ km} $ North of road $ L $ .
Road $ K $ is $ 1\text{ km} $ South of road $ M $ .
If $ K $ is parallel to $ I $ , $ K $ is $ 1/2\text{ km} $ South of $ J $ and $ 1\text{ km} $ North of $ G $ , then which of the following two roads would be $ 1/2\text{ km} $ apart?
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