How to fill geometric figures created by lines and curves?

I'm trying to fill with different colors the 3 triangles in the following graph.

data = data.frame(x=c(125), y=c(220)) #this data is just to be able to use gplot to draw figures

ggplot(data, aes(x = x, y = y)) + 
  xlim(0,250) +
  ylim(-250, 0) +
  geom_curve(x = 33, xend = 223, y = -100, yend = -100, curvature = -.65) +
  geom_segment(x=128, xend = 33, y=-208, yend = -100) +
  geom_segment(x=128, xend = 223, y=-208, yend = -100) +
  geom_segment(x=128, xend = 159.67, y=-208, yend = -45) +
  geom_segment(x=128, xend = 96.33, y=-208, yend = -45) +
  coord_fixed()

How can I do this?