Bisect an angle whose vertex does not fit the page of the diagram.

Question

The question is from Kiselev's Geometry. In the book, I have found two ways to bisect an angle when the vertex $A$ of the angle $BAC$ is given; one is to mark on the other side the segments $AB'=AB$ and $AC'=AC$ then to draw the lines $BC'$ and $B'C$, and the other is to use compass at the vertex. However, I could not find a way to achieve the same goal when the vertex is out of the page and only segments of the sides are given. There was not much of a progress to show here. I wish to know the procedure since it seems like it is required in one of the problems after that.

Answer 1

Take one point from each leg. Join them.

Create the ex-center by constructing the external angle bisectors.

Find the in-center by drawing perpendiculars to the external bisectors.

The line joining the ex- and the in-center is the required.