证明：在AC上取点E,使AE＝AB
∵AD平分∠BAC
∴∠BAD＝∠CAD
∵AB＝AE,AD＝AD
∴△ABD全等于△AED
∴∠AED＝∠B,BD＝DE
∵∠AED＝∠C+∠CDE
∴∠B＝∠C+∠CDE
∵∠B＝2∠C
∴2∠C＝∠C+∠CDE
∴∠C＝∠CDE
∴CE＝DE
∴CE＝BD
∵AC＝AE+CE
∴AC＝AB+BD