第一题如图1,在△ABC中,设ABAC,过点A作△ABC的外接圆的切线l,又以点A为圆心、AC为半径作圆分别交线段AB于点D,交直线l于点E、F.证明:直线图1DE、DF分别通过△ABC的内心与一个旁心.证法1:如图1,作∠BAC的角平分线与DE、FD分别交于点I、I1.由于AC=AD=AE,所以,∠ACI=∠ADI=∠AED The first question is shown in Figure 1, △ ABC, set ABAC, point A for △ ABC of the circumcircle of the tangent l, again with the center of the circle A, AC for the radius of the circle respectively intersects the line segment AB at point D, L at point E, F. Proof: 1DE, DF, respectively, through the center of △ ABC and a side card .Acculus 1: As shown in Figure 1, as BAC angle bisector and DE, FD were at point I, I1. Since AC = AD = AE, ∠ACI = ∠ADI = ∠AED