The southernmost point of the world and the southernmost point on land is the geographic South Pole, which is on the continent of Antarctica.
The point farthest from the Earth's centre is the summit of Chimborazo (due to the Earth not being a perfect sphere), at 6384.4 km (Everest's summit is at 6382.3 km).
The point closest to the Earth's centre (~6353 km) is probably somewhere at the bottom of the Arctic Ocean (depth ~4 km) near the Geographic North pole (the bottom of the Mariana Trench is 6366.4 km from the centre of the Earth).
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