#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let* ((A (point 0 0))
         (B (point '3cm 0))
         (C (point '1cm '2cm))
         (AA (mediation 0.5 B C))
         (BB (mediation 0.5 A C))
         (CC (mediation 0.5 A B))
         (O (unknown-point))
         (polar (unknown-numeric)))
    (eqn= (op- O (mediation 0.5 BB CC))
          (op* (whatever) (rotate 90 (op- BB CC))))
    (eqn= (op- O (mediation 0.5 AA BB))
          (op* (whatever) (rotate 90 (op- AA BB))))
    (draw (op-- A B C 'cycle))
    (for ((x (in-list (list AA BB CC))))
         (draw x #:withpen (scale '4bp 'pencircle )))
    (draw (fullcircle (op* 2 (op-abs (op- O AA)))
                      O))
    (let ((AA (unknown-point))
          (BB (unknown-point))
          (CC (unknown-point))
          (H  (unknown-point)))
      (for ((vAA (in-list (list AA BB CC)))
            (vA (in-list (list A B C)))
            (vB (in-list (list B C A)))
            (vC (in-list (list C A B))))
           (eqn= (op- vAA vA)
                 (op* (whatever) (rotate  90 (op- vB vC))))
           (eqn= vAA (mediation (whatever) vB vC)))
      (for ((vA (in-list (list A B C)))
            (vAA (in-list (list AA BB CC))))
           (draw (op-- vA vAA)))
      (for ((x (in-list (list AA BB CC))))
           (draw x #:withpen (scale '4bp 'pencircle )))
      (eqn= H (mediation (whatever) A AA))
      (eqn= H (mediation (whatever) B BB))
      (for ((x (in-list (list A B C))))
           (draw (mediation 0.5 x H) #:withpen (scale '4bp 'pencircle)))
      )))