题目[1]如图1,在Rt△ABC中,已知CD为斜边AB上的高,I、I1、I2分别为△ABC、△ADC、△BDC的内心,IE⊥AB于点E,直线AI与BC、BI与AC、MN与CD分别交于点N、M、Q.证明QE∥=CI.在文[1]的证明中,作了很多辅助线,使证明过程比较迂回而繁琐.经笔者研究发现,证明此题不须作辅助线,其证明过程简洁而明快. Title [1] As shown in Figure 1, in Rt △ ABC, CD is known as the height of the hypotenuse AB, I, I1, I2 are the center of △ ABC, △ ADC, △ BDC, IE⊥AB at point E, The straight lines AI and BC, BI and AC, MN and CD are respectively intersected by points N, M and Q. Proof QE // = CI. In the proof of [1], many auxiliary lines are made to make the proof process complicated and circuitous After the author study found that proof of this problem need not be a supporting line, which proves that the process is simple and neat.