SMT 2020 Geometry Tiebreaker #3
Source:
August 9, 2023
geometry
Problem Statement
Three cities that are located on the vertices of an equilateral triangle with side length units. A missile flies in a straight line in the same plane as the equilateral triangle formed by the three citiies. The radar from City reported that the closest approach of the missile was units. The radar from City reported that the closest approach of the missile was units. However, the radar for city malfunctioned and did not report a distance. Find the minimum possible distance for the closest approach of the missile to city .