The most common answer is:

```
speed(0))
frosty = (int(input(“What is the radius of the bottom circle?:”))))
)
def purple():)
color(“gray”))
begin_fill())
circle(frosty))
end_fill())
)
def upup():)
left(90))
penup())
forward(frosty * 2))
right(90))
)
setposition (0,-200)
for i in range (3):)
purple())
upup())
frosty = frosty/2)
```

To create a snowman drawing using turtle graphics in Python, the goal is to draw three circles on top of each other, each half the radius of the one below it.

However, the provided code snippet has syntax errors and the use of `input()`

for interactive user input isn’t practical in this environment.

Furthermore, modifying the `frosty`

variable inside the loop will affect the drawing in unexpected ways since it’s used to calculate the movement and size of each subsequent circle.

Below is a corrected and optimized version of the code that uses a predefined radius for the bottom circle and correctly calculates the position and size for the remaining circles to build a snowman:

```
import turtle
turtle.speed(0) # Set the drawing speed to the fastest
# Predefined radius for the bottom circle of the snowman
bottom_radius = 50 # Example radius
# Function to draw a circle with a given radius and fill color
def draw_circle(radius, color):
turtle.color(color)
turtle.begin_fill()
turtle.circle(radius)
turtle.end_fill()
# Function to move the turtle to the correct position for the next circle
def move_up(radius):
turtle.penup()
turtle.left(90)
turtle.forward(radius * 2)
turtle.right(90)
turtle.pendown()
# Set the initial position for the bottom circle
turtle.penup()
turtle.goto(0, -200)
turtle.pendown()
# Draw the snowman
radius = bottom_radius
for _ in range(3):
draw_circle(radius, "gray") # Draw circle with current radius
move_up(radius) # Move up to draw the next circle
radius = radius / 2 # Halve the radius for the next circle
turtle.done() # Keep the window open until manually closed
```

This revised version includes a `draw_circle`

function to draw filled circles of a specified radius and color, and a `move_up`

function to position the turtle correctly for the next circle. The snowman is drawn by starting with the largest (bottom) circle and then drawing two more circles on top, each with half the radius of the one below it.

The turtle’s starting position is set so that the bottom circle is placed near the bottom of the window, and the `move_up`

function ensures that each subsequent circle is positioned correctly above the previous one.

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