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red ant, black ant and termite , shortest possible path, right circular cone

Source: 2022 Chile National Olympiad level 2 p4, level 1 p5

October 22, 2022
geometrygeometric inequalitycone3D geometry

Problem Statement

In a right circular cone of wood, the radius of the circumference TT of the base circle measures 1010 cm, while every point on said circumference is 2020 cm away. from the apex of the cone. A red ant and a termite are located at antipodal points of TT. A black ant is located at the midpoint of the segment that joins the vertex with the position of the termite. If the red ant moves to the black ant's position by the shortest possible path, how far does it travel?