原题目中“求证：AD/DC+AE/ED=1 “这里可能是笔误了,应为“求证：AD/DC+AE/EB=1 ”
如果是这样,证明如下,如果不是则结论难以成立.
证明：
∵ AD/DC = (2CN-DC)/DC = 2CN/DC - 1 = 2(DC-DN)/DC - 1 = 1 - 2DN/DC = 1 - 2PN/BC
AE/EB = (2BM-EB)/EB = 2BM/EB - 1 = 2(EB-EM)/EB - 1 = 1 - 2EM/EB = 1 - 2PM/BC
∴ AD/DC + AE/EB = (1-2PN/BC) + (1-2PM/BC) = 2 - 2(PN/BC+PM/BC) = 2 - 2MN/BC
∵ MN是△ABC的中位线 MN = 1/2 BC
∴ AD/DC + AE/EB = 2 -2*1/2 = 1