Q:

Triangle problem about a point

Question:

If D is a point on the side AB of ABC, find a point X on BC such that the triangles XAD and CAX are equal in area.

My attempt:
I don't actually know how do I solve this problem. I could draw a line parallel to AC from D which may then intersect at X on BC, but that doesn't actually solve the problem.
How do I solve this problem (hints would be great) ?

A:

see if this works. find the midpoint $E$ of $CD$. then the point $X$ you are looking for is point where $AE$ and $BC$ meet.

