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 of the base circle measures cm, while every point on said circumference is cm away. from the apex of the cone. A red ant and a termite are located at antipodal points of . 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?