Gadjo...if you drilled straight down from Bucharesti you would emerge in the South Pacific about a third of the way from NZ to Chile.
Schmenke...Beijing matches up with someplace in Argentina.
Taz..re-read my question...I said 'shortest route' and 'furthest apart'. The ellipsoidal nature of the geoid need not be relevant, as it affects ALL antipodal points by definition.
My question could be re-posed as: Using the shortest route..what's the longest plane ride between 2 capitals?..name them