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题 1 (邹黎明提供 ) △ABC中 ,CD⊥AB于D ,△ACD、△BCD、△ABC的内切圆分别切AC、BC、AB于E、F、G。证明或否定 :∠EGF为直角的充要条件是∠ACB为直角。题 2 (王 勇提供 ) 设实系数多项式 f(x) =xn+an - 1xn - 1+… +a1x +a0 ,令bk=coskπn ,k =0 ,1 ,2 ,… ,n。证明或
Question 1 (provided by Zou Liming) △ABC, CD ⊥ AB in D, △ACD, △BCD, △ ABC inscribed circle cut AC, BC, AB in E, F, G. Proof or Deny: The necessary and sufficient condition for ∠EGF to be a right angle is that ∠ACB is a right angle. Question 2 (provided by Wang Yong) Set the real coefficient polynomial f(x) =xn+an - 1xn - 1+... +a1x +a0 and let bk=coskπn,k=0,1,2,...,n. Proof or