HMMT 二月 2020 · 冲刺赛 · 第 3 题
HMMT February 2020 — Guts Round — Problem 3
题目详情
- [4] Let ABC be a triangle and D , E , and F be the midpoints of sides BC , CA , and AB respectively. What is the maximum number of circles which pass through at least 3 of these 6 points? √ 3 3
解析
- [4] Let ABC be a triangle and D , E , and F be the midpoints of sides BC , CA , and AB respectively. What is the maximum number of circles which pass through at least 3 of these 6 points? Proposed by: Andrew Gu Answer: 17 ( ) 6 Solution: All = 20 triples of points can produce distinct circles aside from the case where the 3 three points are collinear ( BDC , CEA , AF B ). √ 3 3