在一次高二的数学考试中,我出了这样一个题目:已知H为△ABC的垂心,BC=a,AABC的外接圆半径为R,并且a、AH、2R成等差数列。求证:5a=6R 阅卷时,发现一个学生的解法不仅解法简捷,且有新意.现将他的证明略述如下:作△ABC的外接圆O,并作直径CG.连结AO、BG,易证AHBG是平行四边形。则有 In a high school math exam, I came up with such a problem: It is known that H is the vertigo of ΔABC, BC=a, the circumcircle radius of AABC is R, and a, AH, and 2R are equal arithmetic series. Proof: 5a = 6R When you read the paper, you find that a student’s solution is not only simple and straightforward, but also has new ideas. Now his certificate is sketched as follows: Make circumcircle O of ABC, and make diameter CG. Connect AO, BG, and prove AHBG is a parallelogram. There are