本刊数学2098问题为:如图1,⊙O是△ABC的内切圆,D、E、M是切点,连结MO并延长交DE及⊙O分别于点K、F,连结AF、AK并延长分别交BC于点N、L.求证:L是MN的中点.经研究发现,这不仅是圆中的一道综合性较强的试题,还蕴含着圆锥曲线的一般性,现将其推广到圆锥曲线之中,并尝试用解析法给予证明,希望能与读者交流分享.首先,易观察到当⊙O是△ABC的旁切圆时,结论也成立.其次,根据圆可以压缩变换为椭 Mathematics 2098 problem is as follows: Figure 1, ⊙ O is the inscribed circle △ ABC, D, E, M is the tangent point, connecting the MO and extend the intersection of DE and ⊙ O at points K, F, link AF, AK And extend to pay BC at points N, L. Confirmation: L is the midpoint of MN.Through the study found that this is not only a comprehensive test of the round, but also contains the generality of the conic curve, now its To be extended to the conic, and try to prove with analytic method, hoping to share with readers.First, it is easy to observe when ⊙O △ △ ABC circumcircle, the conclusion is also established.Secondly, according to the circle can be compressed transform Ellipse