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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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