题目如图1,已知锐角△ABC满足AB>AC,O、H分别为△ABC的外心、垂心,直线BH与AC交于点B1,直线CH与AB交于点C1.若OH∥B1C1,证明:cos2B+cos2C+1=0.此题是第五届(2014年)陈省身杯全国高中数学奥林匹克第1题,这是一道不落俗套,内涵丰富,解法多样的好题.文[1]中给出了组委会所提供的参考答案,经笔者探究,再给出下面有别于参考答案的新证法. The problem is shown in Figure 1. The acute angle △ABC satisfies AB>AC, O and H are the centers of the heart of △ABC, the lines BH and AC cross at the point B1, and the lines CH and AB cross at the point C1. If OH∥B1C1 , Proof: cos2B+cos2C+1=0. This question is the fifth title (2014) of the National Senior High School Mathematics Olympics title of the first session of the Chen Geng Cup in 2014. This is a good question that is unconventional, rich in content, and diverse in solution. Wen[1] ] gives the reference answers provided by the organizing committee, after the author explored, and then give the following new verification method is different from the reference answer.