How to align circle with 2 pentagons in python using turtle

Question

I am asked to create a program that draws a circle with 2 pentagons: one inside the circle with its vertices are on the circle. the other is outside the circle with its sides tangent to the circle.

I was able to draw the shapes fairly easy, but my problem is aligning them up. Meaning the pentagons are not inside and outside the circle as I was asked.

I don't know much about python, and I feel that this kind of problem needs some math knowledge I do not have.

The code is attached and also a screen shot of what I am getting.

Any help is appreciated.

import random
import math
import re
import turtle
from turtle import Turtle, mainloop
import sys

class KeysMouseEvents:
        def __init__(self):
                super().__init__()
                global arg
                turtle.setup(width=800,height=500,startx=300,starty=250)
                self.T=Turtle()
                self.screen=self.T.getscreen()
                self.T.pensize(4)
                self.T.color("black")
                self.screen.onclick(self.drawconcfigs)
                self.screen.listen()
                self.count=0
                self.first=(0,0)
                self.T.hideturtle()
                self.T.up()
                self.screen.onkey(self.T.clear,"c")
        def drawconcfigs(self,x,y):
                #make turtle fastest speed
                self.T.speed(3)
                #initialize color list
                colorlist = ['red', 'green', 'blue', 'yellow', 'white', 'pink', 'brown', 'purple', 'gray', 'orange']
                #assign random colors for all three shapes
                outersqcolor = random.choice(colorlist)
                circlecolor = random.choice(colorlist)
                while circlecolor  == outersqcolor:
                        circlecolor = random.choice(colorlist)
                innersqcolor = random.choice(colorlist)
                extsquarerot = random.randint(0,90)
                #echo extsquarerot
                intsquarerot = random.randint(0,90)
                degToRads = 0.01745329251
                extsquarerot *= degToRads
                intsquarerot *= degToRads
                while (innersqcolor == circlecolor or innersqcolor == outersqcolor):
                        innersqcolor = random.choice(colorlist)
                #process mouse clicks
                self.count = (self.count + 1)
                if self.count == 1:
                        self.firstx=x
                        self.firsty=y
                        self.T.goto(x,y)
                        self.T.down()
                        self.T.dot()
                        self.T.up()
                        return
                if self.count == 2:
                        #draw rectangle first
                        self.secondx=x
                        self.secondy=y
                        self.T.goto(x,y)
                        self.T.down()
                        self.T.dot()
                        self.T.up()
                        self.count=0
                        X = self.secondx - self.firstx
                        Y = self.secondy - self.firsty
                        d = X * X + Y * Y
                        radius = math.sqrt (d)
                        #L = radius
                        L = math.sqrt(2 * radius * radius)
                        #upperleft = (self.firstx - L * math.cos(extsquarerot), self.firsty + L * math.sin(extsquarerot))
                        side=1.4*radius*math.sin(36)
                        self.T.color("black", outersqcolor)
                        self.T.goto(self.secondx,self.secondy)
                        self.T.right(extsquarerot/degToRads)
                        #self.T.goto(upperleft)
                        self.T.forward(radius)
                        #self.T.goto(self.firstx,self.firsty)
                        #self.T.right(135)
                        self.T.begin_fill()
                        self.T.down()
                        self.T.forward(side)
                        self.T.left(72)
                        self.T.forward(side)
                        self.T.left(72)
                        self.T.forward(side)
                        self.T.left(72)
                        self.T.forward(side)
                        self.T.left(72)
                        self.T.forward(side)
                        self.T.up()
                        self.T.end_fill()


                        #draw circle
                        X = self.secondx - self.firstx
                        Y = self.secondy - self.firsty
                        d = X * X + Y * Y
                        radius = math.sqrt (d);
                        self.T.goto(self.firstx, self.firsty-radius)
                        self.T.color("black", circlecolor)
                        self.T.begin_fill()
                        self.T.down()
                        self.T.setheading(0)
                        self.T.circle(radius)
                        self.T.up()
                        self.T.end_fill()
                        #draw square inside
                        a = math.sqrt (radius*radius/2)
                        upperleft = (self.firstx-a, self.firsty+a)
                        side=radius*math.sin(36)

                        #self.T.goto(upperleft)
                        self.T.color("black", innersqcolor)
                        self.T.goto(self.firstx,self.firsty)
                        self.T.left(intsquarerot/degToRads)
                        #self.T.goto(upperleft)
                        self.T.forward(radius)
                        #self.T.goto(self.firstx,self.firsty)
                        self.T.right(135)
                        self.T.begin_fill()
                        self.T.down()
                        self.T.forward(side)
                        self.T.right(72)
                        self.T.forward(side)
                        self.T.right(72)
                        self.T.forward(side)
                        self.T.right(72)
                        self.T.forward(side)
                        self.T.right(72)
                        self.T.forward(side)
                        self.T.right(72)
                        self.T.up()
                        self.T.end_fill()
                        self.T.goto(self.firstx,self.firsty)
                        self.T.down()
                        self.T.dot()
                        self.T.up()

        def main(self):
                mainloop()

def drawconcfigs():
        draw=KeysMouseEvents()
        draw.main()


if __name__ == '__main__':
        arg=sys.argv[0]
        drawconcfigs()

Thank you, bad result

Answer 1

I created functions so now code is more readable and then I could create working example.

Important elements:

In pentagon()

side = 2*(radius * math.sin(math.radians(36)))

self.T.setheading(0)
self.T.right(144)

and arguments

# draw outer figure
r = radius / math.cos(math.radians(36))
self.pentagon(self.first_x, self.first_y, r, self.outer_color)

# draw circle
self.circle(self.first_x, self.first_y, radius, self.circle_color)

# draw inner figure
r = radius
self.pentagon(self.first_x, self.first_y, r, self.inner_color)

Full working code:

import random
import math
import turtle

class KeysMouseEvents:

    def __init__(self):
        super().__init__()

        turtle.setup(width=800, height=500, startx=300, starty=250)

        self.T = turtle.Turtle()
        self.T.pensize(4)
        self.T.color("black")
        self.T.hideturtle()
        self.T.up()
        self.T.speed(3)

        self.screen = self.T.getscreen()
        self.screen.listen()
        self.screen.onkey(self.T.clear, "c")
        self.screen.onclick(self.on_click)

        self.color_list = ['red', 'green', 'blue', 'yellow', 'white', 'pink', 'brown', 'purple', 'gray', 'orange']
        #print('init')
        self.reset()
        self.select_colors()


    def main(self):
        turtle.mainloop()


    def reset(self):
        self.count = 0
        self.first_x, self.first_y = (0,0)
        self.second_x, self.second_y = (0,0)


    def select_colors(self):
        self.outer_color = random.choice(self.color_list)

        self.circle_color = random.choice(self.color_list)
        while self.circle_color  == self.outer_color:
            self.circle_color = random.choice(self.color_list)

        self.inner_color = random.choice(self.color_list)
        while self.inner_color in (self.circle_color, self.outer_color):
            inner_color = random.choice(self.color_list)


    def distance(self, x1, y1, x2, y2):
        dx = x2 - x1
        dy = y2 - y1
        d = math.sqrt(dx*dx + dy*dy);
        return d


    def dot(self, x, y, color="black"):
        self.T.goto(x, y)
        self.T.color(color, color)

        self.T.down()
        self.T.dot()
        self.T.up()


    def circle(self, x, y, radius, color):
        self.T.goto(x, y-radius)
        self.T.color("black", color)

        self.T.setheading(0)

        self.T.begin_fill()
        self.T.down()
        self.T.circle(radius)
        self.T.up()
        self.T.end_fill()        


    def pentagon(self, x, y, radius, color):
        side = 2*(radius * math.sin(math.radians(36)))

        self.T.goto(x, y+radius)
        self.T.color("black", color)

        self.T.setheading(0)
        self.T.right(144)

        self.T.begin_fill()
        self.T.down()
        for x in range(5):
            self.T.forward(side)
            self.T.left(72)
        self.T.up()
        self.T.end_fill()


    def distance(self, x1, y1, x2, y2):
        dx = x2 - x1
        dy = y2 - y1
        d = math.sqrt(dx*dx + dy*dy);
        return d


    def on_click(self, x, y):

        #process mouse clicks
        self.count += 1

        if self.count == 1:
            self.first_x = x
            self.first_y = y
            self.dot(x,y)
        elif self.count == 2:
            self.second_x = x
            self.second_y = y
            self.dot(x, y)

            # find radius    
            radius = self.distance(self.first_x, self.first_y, self.second_x, self.second_y)

            # draw outer figure
            r = radius / math.cos(math.radians(36))
            self.pentagon(self.first_x, self.first_y, r, self.outer_color)

            # draw circle
            self.circle(self.first_x, self.first_y, radius, self.circle_color)

            # draw inner figure
            r = radius
            self.pentagon(self.first_x, self.first_y, r, self.inner_color)

            # draw points                                 
            self.dot(self.first_x, self.first_y, "red")
            self.dot(self.second_x, self.second_y, "red")

            # reset data                         
            self.reset()
            self.select_colors()



if __name__ == '__main__':
    #draw = KeysMouseEvents()
    #draw.main()
    KeysMouseEvents().main()