Question 144165
Draw the figure.
-----------------------
points at a fixed distance from a point form a circle
--------
points equidistant from the sides of an angle form the bisector of the angle
--------------------
the locus you are looking for could be one of the following:
1) no points if the radius of the circle is less than the perpendicular 
distance from the point to the bisector.
---------
2) one point if the radius of the circle equals the distance from the 
point to the bisector
-------------------------
3) two points if the radius is greater than the perpendicular distance.
===========================
Cheers,
Stan H.