∴BC=DE (equal arc chord)

∫D B C E four-point * * * circle

∴ angle CED+ angle CBD = 180 (four-point * * * circle, diagonally complementary)

Connect DC and BE

∫ arc BC= arc DE (known)

∴ Arc BC+ Arc BD= Arc DE+ Arc BD (equal amount plus equal amount)

∴ arc BE= arc CD (and equal)

∴BE=CD (equal arc chord)

∴△BDE≌△DBC(SSS congruence)

∴ Angle CBD= Angle EDB (the corresponding angles in congruent triangles are equal).

∴ Angle ABD= Angle ADB (complementary angles of equal angles are equal)

∴AB=AD (equilateral)

∴BC+AB=DE+AD (equivalent plus equivalent)

∴AC=AE (and equivalent)