What is reverse triangle inequality?

The reverse triangle inequality states that for any points a, b, and c in a metric space, the absolute value of the difference between the distances from a to c and b to c is less than or equal to the distance from a to b. Mathematically, it is stated as:

|dist(a, c) - dist(b, c)| ≤ dist(a, b)

The reverse triangle inequality is a consequence of the triangle inequality, which states that the sum of any two sides of a triangle must be greater than or equal to the length of the third side. The reverse triangle inequality is used in various branches of mathematics, including analysis, geometry, and optimization, to derive useful inequalities and results.