Creating buffer circle x kilometers from point using Python?

Use a spatial projection library to do the hard work. Adapting from a previous answer, use a dynamic azimuthal equidistant projection to do a geodesic buffer.

from functools import partial
import pyproj
from shapely.ops import transform
from shapely.geometry import Point

proj_wgs84 = pyproj.Proj('+proj=longlat +datum=WGS84')


def geodesic_point_buffer(lat, lon, km):
    # Azimuthal equidistant projection
    aeqd_proj = '+proj=aeqd +lat_0={lat} +lon_0={lon} +x_0=0 +y_0=0'
    project = partial(
        pyproj.transform,
        pyproj.Proj(aeqd_proj.format(lat=lat, lon=lon)),
        proj_wgs84)
    buf = Point(0, 0).buffer(km * 1000)  # distance in metres
    return transform(project, buf).exterior.coords[:]

# Example
b = geodesic_point_buffer(45.4, -75.7, 100.0)

print(b)
# [(-74.42290765358695, 45.39286001598599),
#  (-74.43102886629593, 45.304749544147974),
#  ...
# (-74.42290765358695, 45.392860015985995),
# (-74.42290765358695, 45.39286001598599)]

By using linspace method, from numpy python module, you can use following more concise code:

import numpy as np

bufferLength = 100  # 0.1 km
polygonSides = 360

x = 915884
y = 5042490

angles = np.linspace(0, 2 * np.pi, polygonSides, endpoint=False)
points_list = [(x + np.sin(a) * bufferLength,
                y + np.cos(a) * bufferLength)
               for a in angles]

print(points_list)

where x, y represents an arbitrary point in Ottawa (26917 EPSG code; NAD83/UTM zone 17N)

By using following PyQGIS code (with only 50 points):

import numpy as np

bufferLength = 100
polygonSides = 50

layer = qgis.utils.iface.activeLayer()

points = [feat.geometry().asPoint() for feat in layer.getFeatures()]

epsg = layer.crs().postgisSrid()

angles = np.linspace(0, 2 * np.pi, polygonSides, endpoint=False)
buffer_points = [(points[0][0] + np.sin(a) * bufferLength,
                  points[0][1] + np.cos(a) * bufferLength)
                 for a in angles]

uri = "Point?crs=epsg:" + str(epsg) + "&field=id:integer""&index=yes"

mem_layer = QgsVectorLayer(uri,
                           'buffer_points',
                           'memory')

prov = mem_layer.dataProvider()

feats = [QgsFeature() for i in range(len(buffer_points))]

for i, feat in enumerate(feats):
    feat.setAttributes([i])
    feat.setGeometry(QgsGeometry.fromPoint(
        QgsPoint(buffer_points[i][0], buffer_points[i][1])
    ))

prov.addFeatures(feats)

QgsMapLayerRegistry.instance().addMapLayer(mem_layer)

it can be corroborated that buffer was properly produced: