Of course, you managed this!

 

First, we construct a point A*, such that PA*=PA. Then the angle bisector is the middle perpendicular of AA*.

In my solution, I made the circles partially visible to make the construction clearer. This can be done in the properties dialog of the circle, which opens with a right click on the circle. Moreover, I gave the objects proper names using the name field in the properties dialog of the points.

Move B and see, what happens, when the angle changes, especially, when it becomes larger than 180°.

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