返回题库

HMMT 二月 2009 · 冲刺赛 · 第 6 题

HMMT February 2009 — Guts Round — Problem 6

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

  1. [ 6 ] Let ABC be a right triangle with hypotenuse AC . Let B be the reflection of point B across AC ,
    ′ ′ ′ ′ ′
    and let C be the reflection of C across AB . Find the ratio of [ BCB ] to [ BC B ].
    12 HARVARD-MIT MATHEMATICS TOURNAMENT, 21 FEBRUARY 2009 — GUTS ROUNDth
    3 5 7 9

英文原题

[ 6 ] Let ABC be a right triangle with hypotenuse AC . Let B ′ be the reflection of point B across AC ,
and let C ′ be the reflection of C across AB ′ . Find the ratio of [ BCB ′ ] to [ BC ′ B ′ ].
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12 th HARVARD-MIT MATHEMATICS TOURNAMENT, 21 FEBRUARY 2009 — GUTS ROUND

解析

英文解析

  1. [ 6 ] Let ABC be a right triangle with hypotenuse AC . Let B be the reflection of point B across AC ,
    ′ ′ ′ ′ ′
    and let C be the reflection of C across AB . Find the ratio of [ BCB ] to [ BC B ].
    ′ ′ ′ 1 ′
    Answer: 1 Solution: Since C , B , and C are collinear, it is evident that [ BCB ] = [ BCC ]. It
    ′ ′ ′2
    immediately follows that [ BCB ] = [ BC B ]. Thus, the ratio is 1 .
    12 HARVARD-MIT MATHEMATICS TOURNAMENT, 21 FEBRUARY 2009 — GUTS ROUNDth
    3 5 7 9