方超在《数学通报》2008年第7期问题解答栏第1744题提出如下问题:设h和l是由一个顶点引向对边的高线和角平分线,R和r分别是该三角形外接圆半径和内切圆半径,求证:h/l≥(2r/R)(1/2).(1)原解答似乎过于曲折,难以想到,不易掌握.熟知欧拉不等式R≥2r,因此,(2r/R)(1/2)≤1,但h/l≤1,所以仅用简单的传递性是不行的.而h/l可以用角 Fang Chao In the “Mathematical Bulletin” 2008 the seventh issue of question column No. 1744 questions the following questions: Let h and l from a vertex to the opposite side of the high line and angle bisector, R and r are the triangular external The radius of the circle and the radius of the inscribed circle, verify: h / l≥ (2r / R) (1/2). (1) The original answer seems to be too tortuous, hard to think, not easy to grasp.It is well known Euler’s inequality R≥2r, (2r / R) (1/2) ≤ 1, but h / l ≤ 1, so it is not enough to use only simple transmissibility, while h /