文[1]提出的1720号数学问题内容如下:△ABC中,以BC为轴(长轴或短轴均可)作一椭圆交AB于E,交AC于F.设M、N分别是点E、F关于直线BC的对称点,EN交FM于D.求证:AD⊥BC.文[2]给出了证明方法,之后文[3]、文[4]进行了大篇幅的讨论分析,得出的结论极富美感,但两者推理过程由于计算过于繁琐而稍显不和谐,笔者从极点、极线出发简化文[4]的证明;另 Text [17] proposed the mathematical problem of No. 1720 as follows: △ ABC, the BC axis (long axis or short axis can be) for an elliptical cross AB in E, AC to F. Set M, N are points E, F On the symmetry point of the line BC, EN intersects FM in D. Proof: AD ⊥ BC. [2] gives a proof method, after which the text [3], [4] The conclusion drawn is very aesthetic, but the reasoning process of the two is somewhat inconsistent due to the calculation is too complicated, the author simplifies the proof [4] from the poles and polar lines;