RecursionError when drawing a concentrated circle with Python turtle: How to fix?

How can I fix RecursionError: maximum recursion depth exceeded while calling a Python object error?

I want to draw a concentrated circle inside of trapesoid.In order to do it I used this codeblock below.

I check the condition a+b=c+d ,a b c d are the sides of trapesoid.

What can be the reason of this error?

Here I share my code with you:

import turtle as t
import random as r
p1 = t.Pen()
# parameters
p1.speed(1)
def x1_solve():
x1 = r.randrange(-300, 300)
return x1
def x2_solve():
x2 = r.randrange(-300, 300)
return x2
def y2_solve():
y2 = r.randrange(0, 250)
return y2
def x3_solve():
x3 = r.randrange(x2 + 1, x2 + abs(x1) - 21)
return x3
x1 = x1_solve()
x2 = x2_solve()
y2 = y2_solve()
x3 = x3_solve()
def nums():
global x1,x2,x3,y2
if x1 > 150 or x1 < -150 and x2 > 150 or x2 < -150 and x3 > 150 or x3 < -150:
pass
else:
x1 = x1_solve()
x2 = x2_solve()
y2 = y2_solve()
x3 = x3_solve()
nums()
nums()
if x1 > 0:
side_1 = ((x2 + x1/2)**2 +(y2)**2)**(1/2)
side_2 = ((x3 - x1/2)**2 +(y2)**2)**(1/2)
elif x1 < 0:
side_1 = ((x2 - x1/2)**2 +(y2)**2)**(1/2)
side_2 = ((x3 - abs(x1/2))**2 +(y2)**2)**(1/2)
def a():
global side_1,side_2,x3,x2,x1
if side_1 + side_2 == x3 - x2 + abs(x1):
pass
else:
x3 = x3_solve()
print(x3)
a()
print(side_1)
print(side_2)
a()
p1.goto(x=abs(x1/2),y=0)
p1.pendown()
p1.forward(-1 * abs(x1))
p1.goto(x=x2,y=y2)
p1.goto(x=x3, y=y2)
p1.goto(x=abs(x1)/2,y = 0)
p1.penup()
p1.goto(x=-20,y=-100)
p1.pendown()
p1.write(x3-x2)
p1.penup()
p1.goto(x=-20,y=-120)
p1.pendown()
p1.write(abs(x1))
t.mainloop()

I share my console error with you as well:

Traceback (most recent call last):
File "C:\Users\azaz9\PycharmProjects\pythonProject1\zabit.py", line 52, in <module>
a()
File "C:\Users\azaz9\PycharmProjects\pythonProject1\zabit.py", line 49, in a
a()
File "C:\Users\azaz9\PycharmProjects\pythonProject1\zabit.py", line 49, in a
a()
File "C:\Users\azaz9\PycharmProjects\pythonProject1\zabit.py", line 49, in a
a()
[Previous line repeated 992 more times]
File "C:\Users\azaz9\PycharmProjects\pythonProject1\zabit.py", line 47, in a
x3 = x3_solve()
File "C:\Users\azaz9\PycharmProjects\pythonProject1\zabit.py", line 18, in x3_solve
x3 = r.randrange(x2 + 1, x2 + abs(x1) - 21)
File "C:\Program Files\WindowsApps\PythonSoftwareFoundation.Python.3.10_3.10.3056.0_x64__qbz5n2kfra8p0\lib\random.py", line 352, in randrange
return istart + self._randbelow(width)
File "C:\Program Files\WindowsApps\PythonSoftwareFoundation.Python.3.10_3.10.3056.0_x64__qbz5n2kfra8p0\lib\random.py", line 245, in _randbelow_with_getrandbits
k = n.bit_length()  # don't use (n-1) here because n can be 1
RecursionError: maximum recursion depth exceeded while calling a Python object
Process finished with exit code 1

The problem can be in recursion.However I can not handle this error.

I see a number of issues. First, it appears that this code could fail with an "ValueError: empty range" error if the randomly chosen values for x2 and x1 are too close together:

randrange(x2 + 1, x2 + abs(x1) - 21)

E.g. if x2 is 10 and x1 is 0, then the call randrange(11, -11) fails. Both of your recursive functions could easily be while loops instead:

def a():
global x3
while (side_1 + side_2) != (x3 - x2 + abs(x1)):
x3 = x3_solve()

But that won't stop a runaway calculation. @jasonharper's comment about floating point is spot on (+1) and instead of say a + b == c - d, we'd say something like abs((a + b) - (c - d)) > 0.1

Other things to note is you don't need to raise or lower the pen when you call turtle's write() method, it's independent of the pen. You should reread about what global does as you're over using it. The condition in nums doesn't depend on y2 so there's no reason to recompute it.

I'd approach this by using only positive coordinates until you have it working and then generalize.

It seems that the problem is on the function a() that doesn't have a properly termination condition. You should add a condition for calling back the a() recursively. I post you an example here:

def a():
    global side_1,side_2,x3,x2,x1
    if side_1 + side_2 == x3 - x2 + abs(x1):
        pass
    else:
        x3 = x3_solve()
        print(x3)
        if side_1 + side_2 != x3 - x2 + abs(x1): #here is the added condition
          a()