Typing letters to a text widget by pressing a button in tkinter

I’m trying to type a specific letter into a text box in tkinter by pressing a button with that specific character written on it.

mainmenu = Tk()
mainmenu.title("PROF NAME")
mainmenu.geometry("1200x600")

canvas = Canvas(mainmenu, width = 1200, height = 600)
canvas.pack(fill='both', expand = True)
canvas.create_text(600, 50, text = '교수님의 초성을 입력해주세요', font='Arial 30')

letters = Text(mainmenu, width=20, height=1, font="times 15")
letters.place(x=490, y=140)

def buttonclick():
    letters.insert(END, "ㄱ")

btn1 = Button(mainmenu, padx=2, pady=2, text="ㄱ", font="times 12", command=buttonclick)
btn1.place(x=360, y=90)

So basically the character ㄱ is what I would like to put into the text box ‘letters’ when I press it. What might I be doing wrong here?

Answer

If I understand correctly, this should do what you want it to, but correct me if I’m wrong:

from tkinter import Tk, Canvas, Text, Button, END

mainmenu = Tk()
mainmenu.title("PROF NAME")
mainmenu.geometry("1200x600")

canvas = Canvas(mainmenu, width=1200, height=600)
canvas.pack(fill="both", expand=True)
canvas.create_text(600, 50, text="교수님의 초성을 입력해주세요", font="Arial 30")

letters = Text(mainmenu, width=20, height=1, font="times 15")
letters.place(x=490, y=140)


def button_click(letter):
    return lambda: letters.insert(END, letter)


btn1 = Button(mainmenu, padx=2, pady=2, text="h", font="times 12")
btn1.configure(command=button_click(btn1.cget("text")))
btn1.place(x=360, y=90)

mainmenu.mainloop()