题目(第37届I MO中国选拔赛试题):以△ABC的边BC为直径作半圆,与AB,AC分别交于点D和E,过D,E分别作BC的垂线,垂足分别为F和G,线段DG,EF交于点M.求证:AM⊥BC.本题结论可作如下推广:性质1如图1,以△ABC的边BC为长轴的椭圆交此三角形的另两边AB,AC于点E,F.设M,N分别是点E,F关于直线 Title (37th I MO China Trials Test Questions): to ABC ABC diameter of the circle for the semicircle, and AB, AC were at points D and E, respectively, D, E, respectively, for the BC vertical line, F and G, the line segment DG, EF to point M. Verification: AM ⊥ BC. The conclusion of this question can be used to promote the following: the nature of 1 as shown in Figure 1, with ABC ABC long axis of the ellipse intersect the other two sides of the triangle AB , AC at point E, F. Let M, N point E, F on the straight line