You do not draw any track or great circle on any globe .
Either you draw it on a Jepp Chart or any other chart with similar globe projection.
Or Calculate
Dist= asin ( sin Lat1 x sin Lat 2 + cos Lat 1 x cos Lat 2 x cos ( Long 2- Long 1))
Track Heading will constantly change with the distance....
even if both Lat1 and Lat 2 are on the same paralel....unless they are on equator.
(That is why it was not possible to use it while flying constant heading, before the time of INS etc)
P.S.
Or just use your RNAV computer