第二十三届全国中学生数学冬令营试题及解答
试题:
1.设锐角△ABC的三边长互不相等,O为其外心,点A′在线段AO的延长线上,使得∠BA′A= ∠CA′A,过点A′分别作A′A1⊥AC,A′A2⊥AB,垂足分别为A1,A1,作AHA⊥B C,垂足为HA,记△HAA1A2的外接圆半径为RA,类似地可得RB,RC.求证:1/RA+1/RB+1/RC=2/R.
1.设锐角△ABC的三边长互不相等,O为其外心,点A′在线段AO的延长线上,使得∠BA′A= ∠CA′A,过点A′分别作A′A1⊥AC,A′A2⊥AB,垂足分别为A1,A1,作AHA⊥B C,垂足为HA,记△HAA1A2的外接圆半径为RA,类似地可得RB,RC.求证:1/RA+1/RB+1/RC=2/R.