Verification: AC-AB = 2be.

Test center: the determination and nature of isosceles triangle; Exterior angle properties of triangles.

Comments: This question examines students' understanding and mastery of the judgment and nature of isosceles triangle. Using the theorem of the sum of the inner angles of a triangle and the properties of the outer angles of a triangle, we can examine many knowledge points. It is a difficult problem to solve: proof: extend the intersection of Be and AC to m.

∵BE⊥AE，

∴∠ AEB =∠ AEM = 90 in △ABE，

∫≈ 1+∠3+∠AEB = 180

∴∠3=90 -∠ 1

Similarly, ∠ 4 = 90-∠ 2.

∵∠ 1=∠2,

∴∠3=∠4,

∴AB=AM

∵BE⊥AE，

∴BM=2BE，

∴AC-AB=AC-AM=CM，

∫∠4 is the outer corner of△ △BCM.

∴∠4=∠5+∠C

∵∠ABC=3∠C,∴∠ABC=∠3+∠5=∠4+∠5

∴3∠C=∠4+∠5=2∠5+∠C

∴∠5=∠C

∴CM=BM

∴AC-AB=BM=2BE