#lang racket/base

(define (square x) (* x x))

(define (lengths_eq x1 y1 x2 y2 x3 y3)
(if (equal? (+ (square(- x1 x2)) (square(- y1 y2))) (+ (square(- x3 x1)) (square(- y3 y1)))) 
#t #f
))

(define (collinear x1 y1 x2 y2 x3 y3)
(if (equal? (* (- x1 x2) (- y2 y3)) (* (- y1 y2) (- x2 x3))) 
#t #f
))

(define (perpendicular x1 y1 x2 y2 x3 y3 x4 y4)
(if (equal? (+ (* (- x1 x2) (- x3 x4)) (* (- y1 y2) (- y3 y4))) 0 ) 
#t #f
))



(define (simson o_x o_y a_x a_y b_x b_y c_x c_y d_x d_y e_x e_y f_x f_y g_x g_y)
(if (and 
    (lengths_eq o_x o_y a_x a_y b_x b_y) 
    (lengths_eq o_x o_y a_x a_y c_x c_y) 
    (lengths_eq o_x o_y a_x a_y d_x d_y) 
    (collinear e_x e_y b_x b_y c_x c_y)
    (collinear f_x f_y a_x a_y c_x c_y)
    (collinear g_x g_y a_x a_y b_x b_y)
    (perpendicular b_x b_y c_x c_y d_x d_y e_x e_y)
    (perpendicular a_x a_y c_x c_y d_x d_y f_x f_y)
    (perpendicular a_x a_y b_x b_y d_x d_y g_x g_y))
    
    (begin (displayln "3 Points lie on one line.") (collinear e_x e_y f_x f_y g_x g_y)
    ) (displayln "3 Points do not lie on one line.")
))

(simson 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 )