An algorithm is presented to calculate the point on the surface of a sphere maximising the great-circle distance to a given spherical polygon. This is used to calculate the spots furthest from the sea in major land masses, also known as Poles of Inaccessibility (PIA), a concept that has raised the interest of explorers. For the Eurasian pole of inaccessibility (EPIA), the results reveal a misplacement in previous calculations ranging from 156 to 435 km. Although in general there is only one pole for a given coastline, the present calculations show that, within the error inherent to the definition of the coastline, two locations are candidates for EPIA, one equidistant from Gulf of Ob, Gulf of Bengal and Arabian Sea, and the other equidistant from Gulf of Ob, Gulf of Bengal and Gulf of Bohai, both poles being located in the north westernmost Chinese province of Xinjiang. The distance to the sea at these locations is 2510 and 2514 km respectively, about 120 km closer than generally thought.