HMMT 二月 2008 · GEN1 赛 · 第 10 题

HMMT February 2008 — GEN1 Round — Problem 10

[ 6 ] Let ABC be an equilateral triangle with side length 2, and let Γ be a circle with radius centered at 2 the center of the equilateral triangle. Determine the length of the shortest path that starts somewhere on Γ, visits all three sides of ABC , and ends somewhere on Γ (not necessarily at the starting point). √ Express your answer in the form of p − q , where p and q are rational numbers written as reduced fractions. 1

解析

[ 6 ] Let ABC be an equilateral triangle with side length 2, and let Γ be a circle with radius centered at 2 the center of the equilateral triangle. Determine the length of the shortest path that starts somewhere on Γ, visits all three sides of ABC , and ends somewhere on Γ (not necessarily at the starting point). √ Express your answer in the form of p − q , where p and q are rational numbers written as reduced fractions. √ 28 Answer: − 1 Same as Geometry Test problem 8. 3 2