Intersecting lines with a circle after polar coordinates conversion

Question

I have a dataset in polar coordinates. The dataset contains the coordinates of points that I cast in lines. Then I want to intersect these lines with a circle. From the polar coordinates, you can see that the Boundary of the line is always 18 (which is also the limit of the circle). In order to do the intersect I convert Polar coordinates to cartesian. In the end, only some of the lines correctly intersect the circle, and I do not know why. What works for me is a Not So Elegant Solution: I reduce the circle radius from 18 to 17.999. This works and I suppose that it is because the conversion from polar to cartesian is not 100%. For my purpose, the solution I found is enough, but I want to report it here (I do not know if this is a bug or I made some mistake),

Here is the reproducible example (with plots):

#My Dataset
Boundaries<- data.frame(UE = c(127,127,128,128,128,129,129,129,129,129),
                    ID_Line = c(1,1,1,1,1,1,1,1,2,2), 
                    ID_Point = c(1,2,1,2,3,1,2,3,1,2),
                    Azimut = c(10,120,120,90,230,120,90,230,90,270),
                    Distance = c(18,18,18,5,18,18,5,18,5,18)
                    )

library(tidyverse)
library(useful)

#Polar to Cartesian coordinates conversion
Boundariesxy<-as_tibble(Boundaries) %>%
  mutate(Theta = 2*pi*Azimut/360,
         x = pol2cart(Distance, Theta, degrees=F)[["y"]],
         y = pol2cart(Distance, Theta, degrees=F)[["x"]])


library(sf)
#Conversion to sf object
Boundaries_sf <- st_as_sf(Boundariesxy,
                          coords = c('x', 'y')) %>%
  st_set_crs("102010")  %>%
  group_by(UE, ID_Line)  %>%
  summarise() %>%
  ungroup()

#Cast as Linestring
Bound_lines <- st_cast(Boundaries_sf, "LINESTRING")

#Preparing a circle polygon
Point<- data.frame(
  Plot = c("A"),
  x = c(0),
  y = c(0))
#We convert the center of the circle in a spatial object using a CRS in meters 
Point_sf <- st_as_sf(Point,
                     coords = c('x', 'y')) %>%
  st_set_crs("102010") %>%
  st_convex_hull()
#Buffer 
Circle_st_18<-st_buffer(Point_sf,18)
Circle_st_17999<-st_buffer(Point_sf,17.999)

library(lwgeom)
#For each UE I do an intersect Line->Circle
B127<-Bound_lines[which(Bound_lines$UE==127),]
plot(B127)
Split_127<-st_split(Circle_st_18,B127)
plot(Split_127)
Split_127_2<-st_split(Circle_st_17999,B127)
plot(Split_127_2)
Poly_127 <- (Split_127 %>% st_collection_extract(c("POLYGON")))
st_area(Poly_127)
B128<-Bound_lines[which(Bound_lines$UE==128),]
plot(B128)
Split_128<-st_split(Circle_st_18,B128)
plot(Split_128)
Split_128_2<-st_split(Circle_st_17999,B128)
plot(Split_128_2)
Poly_128 <- (Split_128 %>% st_collection_extract(c("POLYGON")))
st_area(Poly_128)
B129<-Bound_lines[which(Bound_lines$UE==129),]
plot(B129)
Split_129<-st_split(Circle_st_18,B129)
plot(Split_129)
Poly_129 <- (Split_129 %>% st_collection_extract(c("POLYGON")))
st_area(Poly_129)
Split_129_2<-st_split(Circle_st_17999,B129)
plot(Split_129_2)