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Prove that if for {a, b, c} R

  1. Jul 15, 2005 #1
    Problem 1
    Prove that if for {a, b, c} R and all n N there exists
    a triangle with the sides an, bn and cn, then all of these triangles
    are isoscoles.


    Problem 2
    A circle with a radius of 6.25 is circumscribed around a triangle
    with the sides a, b and c. Find these sides, if {a, b, c} N.

    Problem 3
    A line splits a triangle into two new figures with equal perimeters
    and areas. Prove that the center of the inscribed circle lies on this line.


    Problem 4
    The eight lines that connect the vertices of a parallelogram with the
    centers of the two opposite sides form an octogon. Prove that the
    octogon's area is exactly one sixth the area of the parallelogram



    plz guys i'm a new member here can you help me in these geometry problems?
     
  2. jcsd
  3. Jul 15, 2005 #2
    1] Why should it be isosceles?
    Any three sides form a triangle if,
    sum of any two sides is greater than the third side

    Once such a triangle is formed i guess any integer multiple of the lengths work!!
    a+b<c
    then na+nb<nc

    2] Probably some clumsy work in the offing here,
    a/sinA = b/sinB = c/sinC = 2R
    find cosines using the cosine rule, convert them to sines and sub it above.
    So you should find 3 bizarre equations in 3 unknowns, now the biggest trouble is solving them for integer solutions!?!? I am not sure if thats any easier :uhh:

    -- AI
    P.S-> The 3rd question seems interesting, must check it
     
  4. Jul 15, 2005 #3
    thanx tenaliraman
     
  5. Jul 15, 2005 #4
    any 1 for 3 and 4
     
  6. Jul 23, 2005 #5
    problem 3
    works only with equilateral triangles
     
  7. Jul 23, 2005 #6
    come to think of it. doesnt work at all.
     
  8. Jul 24, 2005 #7

    VietDao29

    User Avatar
    Homework Helper

    Ebn_Alnafees, you should give the problems a try and post as much of your work as possible here. Read the sticky thread.
    Problem 3: Hint : Draw one bisector that cut the line. Call the intersection of that bisector and the line E. What do you reckon? If the line cuts 2 legs AB (at F), and AC (at G), then the bisector should go through A, so the distance between E and AB, AC is the same.
    Use what the problem tells you : The two new figure have the same perimeters and area.
    Hope you get it.
    Viet Dao,
     
    Last edited: Jul 24, 2005
  9. Jul 24, 2005 #8
    can you email me the answer. from how i understand the question. there's no solution. except the special cases of isosolese and equilateral triangles split congruently.
     
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