The question is that:
Let $ABCD$ be a parallelogram. Let $X$ and $Y$ be points on $AB$ and $BC$ respectively, such that $AX=CY$. Prove that the intersection of lines $AY$ and $CX$ lies on the angle bisector of $\angle ADC$.
I have put the parallelogram on coordinate plane and proved that. However, are there any way such that it can be solved algebraically?