丁遵标老师在《数学通报》2 0 0 0年第 6期 ,用三角法给出了欧拉不等式的一种巧妙证法 ,读后深受启发 ,现笔者应用点线距离的性质给出一种更为简捷的证法 .欧拉不等式　若三角形的外接圆的半径为R ,内切圆的半径为r,则R ≥ 2r.证明　设三角形ABC的三边长分别为a ,b,c,面积为S , In the sixth issue of the “Medical Bulletin” 2000, the teacher Ding Zongbiao gave a clever demonstration of Euler’s inequality by using the trigonometry method. After reading it, he was deeply inspired. Now the author uses the nature of the distance between points to give a kind of A simpler proof method. Euler inequality If the radius of the circumscribed circle of the triangle is R, and the radius of the inscribed circle is r, then R ≥ 2r. Prove that the trilateral length of the triangle ABC is a, b, c, respectively. For S,