Flee the Disease

author: Satyarth Mishra Sharma

There's a disease in three cities, which we literally need to flee from. This means finding a city which is farthest from Abidjan, Manila, and Auckland. One could write their own program to do so, or just use a tool online.

Some possible ways to solve:

• Vector algebra: find the circumcenter of the triangle formed by the three cities. This represents the closest point equidistant from the three cities, and its antipode gives the furthest point. Hint: just like on a plane, the cirumcenter is the intersection of the perpendicular bisectors (of the three geodesics connecting the three points).

• Brute force it: find a DB of major cities and coordinates, write a function to calculate distances on a sphere, iterate through and maximize the minimum distance from one of the three cities.

• Google around and find this tool that draws Voronoi diagrams on top of a world map.

The solution was Boise.