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Harbin junior high school mathematics
The two are actually very similar.

Solution: The vertical line with E'C passing through point B intersects its extension line at point F, the vertical line with CM passing through point D intersects it at point H, and the vertical line with CM passing through point A intersects its extension line at point G. 。

∠∠ACD ' = 60,∠D'CE'=90,

∴∠ACE'=30

∠∠ACB = 90,∠ FCE' = 180。

∴∠BCF=∠FCE'-∠ACB-∠ACE'=60,

BF=sin∠BCF? BC=5√3

∴S△BCE'= 1/2? BF? CE'= 15√3

∠∠ACG+∠BCN = 90,∠BCN+∠CBN=90,

∴∠ACG=∠CBN

AC = BC,

∴Rt△ACG≌Rt△CBN,

∴AG=CN,CG=BN.

Similarly △ CD ′ h △ ce ′ n, d ′ h = cn, CH = NE' ′.

∴M is the midpoint of GH, and cm =1/2 (CG+ch) =1/2be'.

And ∵BF=5√3, ∠ BCF = 60,

∴cf=5,fe′=cf+ce′= 1 1,

∴BE'=√(BF^2+FE'^2)= 14,

∴CM= 1/2BE'=7.

∫S△BCE ' = 1/2? CN? Yes,

∴cn=2s△bce′÷be'= 15√3/7

∴MN=CM-CN=7- 15√3/7

Finally finished ...?