一道数学几何体急急急 20
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小妹妹,这是不是初中数学竞赛?
CE=DF,根据相似原理,CF和BE垂直且相等;
设 CE = DF = x,
BE = 根(49+x^2)
根据题目:BE=CF=CM+MN+FN = 2MC+4CM/3 = 10CM/3
根据等面积原理:BE × CM = 7x
10/3 × 7x / BE = 10CM/3 = BE
BE^2 = 70x / 3 = 49 + x^2
解得:x=7/3 或者 21(舍掉)
BE = CF = 根(49+x^2)=7根10 / 3
CM = 7/根10
cos∠AFN = - cos∠CFD = - (7/3) / (7根10 / 3) = -1/根10
AF = 14/3
FN = 4CM / 3 = 28 / (3根10)
用余弦定理可得:
AN = 14 / 根5
CE=DF,根据相似原理,CF和BE垂直且相等;
设 CE = DF = x,
BE = 根(49+x^2)
根据题目:BE=CF=CM+MN+FN = 2MC+4CM/3 = 10CM/3
根据等面积原理:BE × CM = 7x
10/3 × 7x / BE = 10CM/3 = BE
BE^2 = 70x / 3 = 49 + x^2
解得:x=7/3 或者 21(舍掉)
BE = CF = 根(49+x^2)=7根10 / 3
CM = 7/根10
cos∠AFN = - cos∠CFD = - (7/3) / (7根10 / 3) = -1/根10
AF = 14/3
FN = 4CM / 3 = 28 / (3根10)
用余弦定理可得:
AN = 14 / 根5
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