Let P be any point in the interior of circle O except O itself. Show that the shortest cho...

Let P be any point in the interior of circle O except O itself. Show that the shortest chord containing P must be the one where  is perpendicular to the chord.

(Hint: Draw chord  where P is on  and  is perpendicular to . Then draw any other chord  through point P. Then consider the perpendicular segment  from O to .)