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1991年中国数学奥林匹克(CMO),即第六届全国中学生数学冬令营,于1991年1月11日至15日在武汉市华中师范大学举行。1月12日及13日上午各用4.5小时进行竞赛考试,与此同步还用同一份试题进行了第二届陈省身杯团体赛(部分省、市、自治区各派出3名营员参赛)。下面是这次竞赛的6道试题及解答。(每题满分21分,最高得分为117分) 第一天 (1991年1月12日上午8:00—12:30) 一、平面上有一个凸四边形ABCD, (1)如果平面上存在一点P,使得
In 1991, the Chinese Mathematics Olympiad (CMO), the sixth mathematics winter camp for middle school students, was held at Huazhong Normal University in Wuhan from January 11th to 15th, 1991. On the morning of January 12th and on the morning of the 13th, they took a 4.5-hour contest to take the exam. In conjunction with this, they also used the same question for the second Chenshen Cup Team competition (parts of each province, city, and autonomous region sent 3 campers to compete). Here are 6 questions and answers for this competition. (21 points for each question, the highest score is 117 points) The first day (January 12, 1991, 8:00-12:30 am) 1. There is a convex quadrilateral ABCD in the plane. (1) If there is a point on the plane P, so that