import arcpy, math
arcpy.env.overwriteOutput = True

#Change to match your data:
arcpy.env.workspace = r'C:ArendenDefault.gdb'
boundries = r'Boundries'
points = r'bufferpoints'
out_feature_class = r'GrowPoints'

#Change to match your desired size of polygon, ok difference and step in buffer radius increase
size = 7500
ok_diff = 500
increment = 5


arcpy.CreateFeatureclass_management(out_path=arcpy.env.workspace, out_name=out_feature_class,
                                   geometry_type='POLYGON',
                                   spatial_reference=arcpy.Describe(points).spatialReference)

arcpy.MakeFeatureLayer_management(in_features=boundries, out_layer='blyr')

with arcpy.da.SearchCursor(points,['OID@','SHAPE@']) as cursor:
    for row in cursor:
        bufferstart = math.sqrt((size/math.pi))
        sql = """{0} = {1}""".format(
            arcpy.AddFieldDelimiters(points,arcpy.Describe(points).OIDFieldName),row[0])
        arcpy.MakeFeatureLayer_management(in_features=points, out_layer='pointlyr',where_clause=sql)
        arcpy.SelectLayerByLocation_management(in_layer='blyr', overlap_type='INTERSECT',
                                              select_features='pointlyr')
        if [i[0] for i in arcpy.da.SearchCursor('blyr','SHAPE@AREA')][0] > size:
            area = 1
            while abs(size-area)>ok_diff:
                print area
                arcpy.Buffer_analysis(in_features='pointlyr', out_feature_class=r'in_memorypoint',
                                     buffer_distance_or_field="{0} Meters".format(bufferstart))
                arcpy.Clip_analysis(in_features=r'in_memorypoint', clip_features='blyr',out_feature_class=r'in_memoryclipbuffer')
                area = [i[0] for i in arcpy.da.SearchCursor(r'in_memoryclipbuffer','SHAPE@AREA')][0]
                bufferstart+=increment

            arcpy.Append_management(inputs=r'in_memoryclipbuffer', target=out_feature_class, schema_type='NO_TEST')
        else:
            print 'Impossible to fit buffer inside boundry for point number: ',row[0]