I'm trying to tackle the following question, but unfortunately anything I tried got to a dead end (area of triangle, circles, angle bisectors, etc...) and I'm totally clueless how to solve it...
Let $P$ be some point on the side of given $\triangle ABC$ (WLOG, let $P$ be on BC).
Construct a line which passes through $P$ and halves the area of the triangle.
Please give some hints. Thank you!