Solution: As shown in the following figure, the vertical line intersecting with point B in the form of E'C intersects with its extension line at point F, the vertical line intersecting with point D 'in the form of CM intersects with it at point H, and the vertical line intersecting with point A in the form of CM intersects with its extension line at point G. 。

∠∠ACD ' = 60，∠ACB=∠D'CE'=90，

∴∠bce=360-∠ACD '-∠ACB-∠d ' ce ' = 120。

∴∠BCF= 180 -∠BCE=60，BF=sin∠BCF？ BC=5√3，CF=5

∴EF= 1 1 Pythagorean theorem can be found as' = 14.

It can be proved that CN= 15/7√3, NE'=33/7 and BN=65/7 can be found in △ CNE' ∩△ be 'f.

Yi Zheng △ CNE '△ CHD', △ BCN △ CAG

∴ag=cn=d'h= 15/7√3,bn=cg=65/7,ne'=ch=33/7

It is proved that △ AGM ≌△ D 'hm, △ GM = hm =16/7.

∴CM=HM+CH=7

∴MN=7+ is a triple 15 root sign.

Similarly, when △D'CE' is inside △ACB, MN=7- 15/7√3?

PS: Do you want to give some branches in order to write so much?