You can
put this solution on YOUR website!Draw the figure.
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points at a fixed distance from a point form a circle
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points equidistant from the sides of an angle form the bisector of the angle
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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.
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2) one point if the radius of the circle equals the distance from the
point to the bisector
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3) two points if the radius is greater than the perpendicular distance.
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Cheers,
Stan H.