21aditya , u deleted ur post but that was a good guess ..;)
Let ABC be the triangle formed by intersection of the lines x-y=0 , y=0 and 7x+y = 56. Find the minimum possible perimeter of the family of triangles inscribed in ABC.
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9 Answers
21really good idea...
try and prove that it will be the pedal triangle wich has minimum perimeter
21oh sorry..it is not the pedal triangle that has minimum perimeter....i was wrong.. and aditya ur guess was not good.. :D
1Actually , this problem was discovered and solved by Fagnano in 1755 , fom which point onwards it became known as Fagnano ' s problem . Of all the triangles that can be inscribed in a given acute triangle , the one that possesses the least perimeter is the " orthic triangle " of the given triangle . Given below is a link to one of the most basic possible solutions to this problem -
www.math.uoc.gr/~pamfilos/eGallery/problems/Fagnano2.html
21yes...this days this kind of qstns r frequently seen in aits ...so i was studying transformational geometry (after 5 yrs lol)..the titus book geom. probs on maxima minima gave a sol. given by L.fezer in 1900......btw cudnt find any link on internet..
1However , it would do much good if , here , someone explicitly derives the formula for the perimeter of an orthic triangle in terms of the variables used to " define " the original triangle .