HMMT 二月 2002 · 冲刺赛 · 第 46 题
HMMT February 2002 — Guts Round — Problem 46
题目详情
- [ ± 6] Points A, B, C in the plane satisfy AB = 2002 , AC = 9999. The circles with diameters AB and AC intersect at A and D . If AD = 37, what is the shortest distance from point A to line BC ?
解析
- Points A, B, C in the plane satisfy AB = 2002 , AC = 9999. The circles with diameters AB and AC intersect at A and D . If AD = 37, what is the shortest distance from point A to line BC ? 11 Solution: ∠ ADB = ∠ ADC = π/ 2 since D lies on the circles with AB and AC as diameters, so D is the foot of the perpendicular from A to line BC , and the answer is the given 37 .