2006 IMO Shortlist G3

Let $A B C D E$ be a convex pentagon such that $$\angle B A C=\angle C A D=\angle D A E \quad \text { and } \quad \angle A B C=\angle A C D=\angle A D E \text {. }$$ The diagonals $B D$ and $C E$ meet at $P$. Prove that the line $A P$ bisects the side $C D$.

令 $A B C D E$ 为凸五边形，使得 $$\angle B A C=\angle C A D=\angle D A E \quad \text { 和 } \quad \angle A B C=\angle A C D=\angle A D E \text { 。 }$$ 对角线$B D$ 和$C E$ 相交于$P$。证明线 $A P$ 平分边 $C D$。