I am using 9.3.1. Attaching the shape files that I used in UTM projection
1)Points.shp---My features of interest
2)BoundingBox.shp----Envelope for above points
3)BoundingBox_Centroid.shp---Centroiod of this envelope
4)BoundingBox_Centroid_Generat.dbf---Near table created by Proximity Analysis tool
5)BoundingCircle.shp---Buffer created using largest distance(3582.146565 meters in this case)
FID 1275 is the farthest vertex in Points.shp from centroid ..this seems to lie oust side the BoundingCircle
I noticed an interesting thing...I have used 'Smooth' tool from Advanced Editing feature,with a threshold of 0.09(which is the measured deviation from circle boundary to the outlier point).This is resulting in a circle that passes through the outlier point just as I need.
Unfortunately,this is true only during editing session.The changes get lost when I save the changes brought in by 'smooth' .