MathDB
Equilateral Triangle Path

Source:

March 9, 2008
inequalitiesgeometrygeometric transformationreflectiontriangle inequality

Problem Statement

Let ABC ABC be an equilateral triangle with side length 2, and let Γ \Gamma be a circle with radius 12 \frac {1}{2} centered at the center of the equilateral triangle. Determine the length of the shortest path that starts somewhere on Γ \Gamma, visits all three sides of ABC ABC, and ends somewhere on Γ \Gamma (not necessarily at the starting point). Express your answer in the form of \sqrt p \minus{} q, where p p and q q are rational numbers written as reduced fractions.
Back to ProblemsView on AoPS