21oh sorry..it is not the pedal triangle that has minimum perimeter....i was wrong.. and aditya ur guess was not good.. :D
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
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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 .