Finding the radius of a circle that circumscribes a polygon - r

Question

I am trying to find the best way of obtaining: the length of the longest line from the center of a polygon to its edge.
In the code below, I download the polygon data of the 75254 zip code located in Texas, USA. I then determine the location of its center with sf::st_centroid() and I plot the geometries using the tmap package.
# Useful packages
library(dplyr)
library(sf)
library(tigris)
library(tmap)
# Download polygon data
geo <- tigris::zctas(cb = TRUE, starts_with = "75254")
geo <- st_as_sf(geo)
# Determine the location of the polygon's center
geo_center <- st_centroid(geo)
# Plot geometries
tm_shape(geo) +
tm_polygons() +
tm_shape(geo_center) +
tm_dots(size = 0.1, col = "red")
Once again, is there an efficient way to determine the length of the line going from the center of the polygon all the way to the farthest point on the polygon's edge? In other words, how can I find the radius of the circle that perfectly circumscribes the polygon given that both the circle and the polygon have the same center?
Thank you very much for your help.

Answer 1

One point here, although I mentioned, st_bbox wouldn't work as the centroid of the bbox and the one of your shape are not the same, since the centroid is weighted. See here one approach based on the further distance to the points of the border, but you woud need to project your shape (currently is unprojected):
library(dplyr)
library(sf)
library(tigris)
library(tmap)
# Download polygon data
geo <- tigris::zctas(cb = TRUE, starts_with = "75254")
geo <- st_as_sf(geo)
st_crs(geo)
#> Coordinate Reference System:
#> EPSG: 4269
#> proj4string: "+proj=longlat +ellps=GRS80 +towgs84=0,0,0,0,0,0,0 +no_defs"
#Need to project
geo=st_transform(geo,3857)
# Determine the location of the polygon's center
geo_center <- st_centroid(geo)
#> Warning in st_centroid.sf(geo): st_centroid assumes attributes are constant over
#> geometries of x
plot(st_geometry(geo))
plot(st_geometry(geo_center), col="blue", add=TRUE)
#Cast to points
geopoints=st_cast(geo,"POINT")
#> Warning in st_cast.sf(geo, "POINT"): repeating attributes for all sub-geometries
#> for which they may not be constant
r=max(st_distance(geo_center,geopoints))
r
#> 3684.917 [m]
buffer=st_buffer(geo_center,dist=r)
plot(st_geometry(buffer), add=TRUE, border="green")

Answer 2

OP didn't ask for this, but in case anyone else would like to do this for multiple shapes, here's a version that builds on dieghernan's example to do that.
library(dplyr)
library(sf)
library(tigris)
library(tmap)
# Download polygon data
raw <- tigris::zctas(cb = TRUE, starts_with = "752")
geo <- raw %>%
st_as_sf() %>%
slice(1:5) %>%
st_transform(3857) %>%
arrange(GEOID10) # Sort on GEOID now so we don't have to worry about group_by resorting later
# Compute the convex hull
hull <- geo %>% st_convex_hull()
# Compute centroids
geo_center <- st_centroid(geo)
# Add centroid, then cast hull to points
hull_points <- hull %>%
mutate(centroid_geometry = geo_center$geometry) %>%
st_cast("POINT")
# Compute distance from centroid to all points in hull
hull_points$dist_to_centroid <- as.numeric(hull_points %>%
st_distance(hull_points$centroid_geometry, by_element = TRUE))
# Pick the hull point the furthest distance from the centroid
hull_max <- hull_points %>%
arrange(GEOID10) %>%
group_by(GEOID10) %>%
summarize(max_dist = max(dist_to_centroid)) %>%
ungroup()
# Draw a circle using that distance
geo_circumscribed <- geo_center %>% st_buffer(hull_max$max_dist)
# Plot the shape, the hull, the centroids, and the circumscribed circles
tm_shape(geo) +
tm_borders(col = "red") +
tm_shape(hull) +
tm_borders(col = "blue", alpha = 0.5) +
tm_shape(geo_center) +
tm_symbols(col = "red", size = 0.1) +
tm_shape(geo_circumscribed) +
tm_borders(col = "green")