返回题库

HMMT 二月 2002 · 冲刺赛 · 第 46 题

HMMT February 2002 — Guts Round — Problem 46

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [ ± 6] Points A, B, C in the plane satisfy AB = 2002 , AC = 9999. The circles withdiameters AB and AC intersect at A and D . If AD = 37, what is the shortest distance frompoint A to line BC ?
解析

英文解析

  1. Points A, B, C in the plane satisfy AB = 2002 , AC = 9999. The circles withdiameters AB and AC intersect at A and D . If AD = 37, what is the shortest distance frompoint A to line BC ?
    Solution: ∠ ADB = ∠ ADC = π/ 2 since D lies on the circles with AB and AC as 11
    diameters, so D is the foot of the perpendicular from A to line BC , and the answer is thegiven 37 .