Question

如图,四边形ABCD内接于圆O,AD,BC的延长线交于点E,点F在BD的延长上线上,且DE平分角CDF.

Answer 1

∵DE平分∠CDF,∴∠EDF=∠EDC,

∵∠ACB=∠ADB=∠EDF,

∠ABC=∠EDC,

∴∠ABC=∠ACB,

∴AB=AC.

⑵ΔEDC∽ΔEBA,

ΔEDB∽ΔECA.

ΔEDC∽ΔBDA,

ΔEBA∽ΔBDA,

⑶∵ΔEBA∽ΔBDA,

∴AB/AD=AE/AB,又AB=AC=3,

∴AE=AB^2/AD=4.5,

∴DE=AE-AD=2.5.