Размеры прямоугольника в который вписана дуга

from math import *
 
#Точка начала дуги
a = {'x': 6.31, 'y': 5.773}
#Точка конца дуги
b = {'x': 20.53, 'y': 19.836}
#Центр окружности (дуги)
c = {'x': 13.42, 'y': 12.805}
 
    
def arcRadius(a, b, c):
    radius = sqrt((a['x'] - c['x'])**2 + (a['y'] - c['y'])**2)
    return radius
        
def arcAngles(a, b, c):
    startAngle = atan2((a['y'] - c['y']), (a['x'] - c['x']))
    endAngle = atan2((b['y'] - c['y']), (b['x'] - c['x']))
    spanAngle = endAngle - startAngle
    if spanAngle < 0:
        spanAngle = endAngle + (2 * pi)
    if spanAngle >= (2 * pi):
        spanAngle = spanAngle - (2 * pi)
    return (startAngle, endAngle, spanAngle)
   
def arcHeight(radius, spanAngle):
    height = 2 * radius * sin(spanAngle / 4)**2
    return height
    
R = arcRadius(a, b, c)
print("Radius: " + str(R))
startAngle, endAngle, spanAngle = arcAngles(a, b, c)
print("startAngle: " + str(startAngle) + "\nendAngle: " + str(endAngle) + "\nspanAngle: " + str(spanAngle))
h = arcHeight(R, spanAngle)
print("Arc height: " + str(spanAngle))
fi = (endAngle + startAngle) / 2
dx = h * cos(fi)
dy = h * sin(fi)
 
#p1 - p4 точки прямоугольника
if spanAngle <= pi:
    p1x = a['x']
    p1y = a['y']
    p2x = b['x']
    p2y = b['y']
    p3x = p2x + dx
    p3y = p2y + dy
    p4x = p1x + dx
    p4y = p1y + dy
else:
    xsx = (a['x'] + b['x']) / 2
    ysx=(a['y'] + b['y']) / 2
 
    Lx = sqrt((a['x'] - b['x'])**2 + (a['y'] - b['y'])**2)
 
    p1x = (a['x'] - xsx) * 2 * R / Lx + xsx
    p1y = (a['y'] - ysx) * 2 * R / Lx + ysx
    p2x = (b['x'] - xsx) * 2 * R / Lx + xsx 
    p2y = (b['y'] - ysx) * 2 * R / Lx + ysx
    p3x = p2x + dx 
    p3y = p2y + dy
    p4x = p1x + dx 
    p4y = p1y + dy
  
print("-----------Rectangle points-------------")
print(p1x, p1y)
print(p2x, p2y)
print(p3x, p3y)
print(p4x, p4y)