如图1,⊙O1与⊙O2交于A、B两点,延长O1A交⊙O2于点C,延长O2A交⊙O1于点D,过点B作BE∥O2A交⊙O1于点E,若DE∥O1A,求证:DC⊥CO2.这是2014年中国女子数学奥赛第一题,笔者从多角度来添设辅助线证明本题,供同学们参考.证法一如图1,分别连接DB、O1O2、AB,延长EB交⊙O2于H,连接AH.∵∠ABH=∠EDA=∠O1AO2=∠DAB, As shown in Figure 1, ⊙ O1 and ⊙ O2 to pay A, B two points, to extend O1A to pay ⊙ O2 at point C, extend O2A to pay ⊙ O1 at point D, to point B BE ∥ O2A to pay ⊙ O1 at point E, if DE ∥ O1A, verify: DC ⊥ CO2. This is the first issue of China Women’s Mathematical Olympiad in 2014, the author from the multi-angle to add auxiliary line to prove the problem, for the students to refer to .Activities as shown in Figure 1, respectively, O1O2, AB, extend the intersection of EB and cross ⊙ O2 at H, connect AH.∵∠ABH = ∠EDA = ∠O1AO2 = ∠DAB,