As a first try, we arrived that shape:
Pre calculated distances:
Los Angeles - Atlanta: 3.073kms. +-7%
Los Angeles - Chicago : 2.769kms. +-3%
Atlanta - Chicago: 1.221 kms. +-7%
Dallas- Los Angeles: 2.168kms. +-12%
Dallas- Atlanta: 1369 kms. +-6%
Dallas - Chicago: 1.583kms. +-8%
Distances on the map:
Los Angeles - Atlanta: 3.074 kms
Los Angeles - Chicago : 2.769 kms
Atlanta - Chicago: 1.222 kms
Dallas- Los Angeles: 2.028 kms
Dallas- Atlanta: 1.230 kms
Dallas - Chicago: 1.723 kms
Distances map/calculated/Average mistake
3.073/3.074 = 0%
2.769/2.769 = 0%
1.221/1.222 =0%
2.168/2.028 = 7%
1369/1230 = 11%
1583/1723= 9%