Geometry problem in Hironaka Heisuke's book. (I don't think this book is translated into English.) I saw this beautiful problem which the author said he solved it in high school:
$P$ is a point outside of $\triangle ABC$, $\ell$ is a line crossing $P$ and splits $\triangle ABC$ into $\triangle ADE$ and $\square DEBC$.
Construct $\ell$ which makes $\overline{DB} \cong\overline{EC}$.
I have tried making $\triangle ABC$ an isosceles triangle, which makes this problem very easy. (Make $\overline{BC} \parallel \overline{PE}$.)
But if $\triangle ABC$ becomes a normal triangle like in the picture, all I can guess is that $\overline{PE}$ has to be a bit diagonal.
I disagree with this question being closed. I saw a similar question from the link (Constructing a line that passes through $P$).
But, I have a more detailed explanation with a picture.
Second, the solution to the question didn't contain an explanation with pictures, so I wanted more detailed answers. (the second answer includes a picture but he said it is not a solution)
Lastly, I added my try of solving different from the original question.