buffer-test.js

var turf = require('turf');

turf.load('3m-buffered-point.geojson', function (err, data) {
  var features = data.features,
    point = features[0],
    poly = turf.buffer(point, 3, 'miles'),
    polyCoords;

  polyCoords = poly.features[0].geometry.coordinates[0];

  for (var i = 0, len = polyCoords.length; i < len; i++) {
    var coords = polyCoords[i],
      vertexPoint = turf.point(coords[0], coords[1]),
      distance = turf.distance(point, vertexPoint, 'miles');

    console.log(distance)
  }
})

/* Output:
3.0029561767624524
2.9769050459117814
2.9014525901415698
2.78473931203686
2.640472647335498
2.487881005444849
2.350793943903439
2.2545636090512726
2.21978422493748
2.2545636090512726
2.350793943903439
2.487881005444849
2.640472647335498
2.78473931203686
2.9014525901415698
2.9769050459117814
3.0029561767624524
2.9768965537986483
2.901386827178415
2.784529649109837
2.6400167324747987
2.487094229412039
2.349651565716341
2.253138429788066
2.2182499180461144
2.253138429788066
2.349651565716341
2.487094229412039
2.6400167324747987
2.784529649109837
2.901386827178415
2.9768965537996195
3.0029561767624524
*/