Directional Buffer increasing radius of geometry

all you need to do is a scale transformation with the center of the pie as the center of scale. however the distances will be scaled approximately, since my solution is only based on Euclidean distances scaling. it doesn't account for the curvature of the earth whatsoever.

for example, with pandas:

import pandas as pd
from shapely.geometry import Point, LineString, Polygon
import geopandas as gp

data = [[1,72.774906,27.620367],[1,72.983647,27.707941],[1,73.148441,27.785725],[1,73.280277,27.853741],[1,73.401127,27.921714],[1,73.467045,27.795445],
[1,73.510990,27.737117],[1,73.521977,27.659298],[1,73.500004,27.581423],[1,73.478031,27.552206],[1,73.467045,27.503493],[1,73.434086,27.454759],
[1,73.412113,27.406003],[1,72.774906,27.620367]] 
df_poly = pd.DataFrame(data, columns = ['poly_ID','lon', 'lat']) 


translation = data[0] # center of the pie of your polygon 

scale_data = [
    1, # don't scale the poly_ID
    2, # scale by 2 the longitude distances
    2  # scale by 2 the latitude distances
]
scale = pd.Series(scale_data, index= ['poly_ID','lon', 'lat'])

df_translated_poly = df_poly.sub(translation) # center your transform on the center

df_translated_scaled_poly = df_translated_poly.mul(scale) # scale your polygon

df_scaled_poly = df_translated_scaled_poly.add(translation) # re-transform back in the original place


lat = df_poly.lat.tolist()
lon = df_poly.lon.tolist()
polygon_geom = Polygon(zip(lon, lat))

lat = df_scaled_poly.lat.tolist()
lon = df_scaled_poly.lon.tolist()
polygon_geom_scaled = Polygon(zip(lon, lat))


crs = {'init': 'epsg:4326'}
polygon = gp.GeoDataFrame(index=[0, 1], crs=crs, geometry=[polygon_geom, polygon_geom_scaled])       

import folium
m = folium.Map([50.854457, 4.377184], zoom_start=5, tiles='cartodbpositron')
folium.GeoJson(polygon).add_to(m)
folium.LatLngPopup().add_to(m)
m