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Math Help - Geometry Marathon

  1. #16
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    If your proof doesn't use trig. then it's okay.
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  2. #17
    Senior Member OReilly's Avatar
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    Quote Originally Posted by blurgh View Post
    i've figured out the solution but the proof doesn't use similar triangles.
    Post your solution.
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  3. #18
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    Talking my proof

    correction, my proof does use similar triangles. i found a mistake in my proof and had to fix it. (hehe, oops)
    um, i haven't got the hang of Latex, so i hope you don't mind if i give you a link to a pdf file instead. (you'll have to download it, sorry!)
    although i think and am more fluent in English, i always solve math problems in Vietnamese, so my proof is basically a literal translation of what i would've written in Vietnamese, so I'm sorry if it doesn't make sense in some parts. All symbols are what the Vietnamese use in our math, if there is anything different from what most people would write please tell me.
    once again, sorry for making you download a pdf file.


    my proof
    Last edited by blurgh; June 23rd 2007 at 11:42 PM.
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  4. #19
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    impressive proof!
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  5. #20
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    Nice proof.

    You can shorten it using similar triangles.

    In your sketch we have that \overline{AD}=\overline{CD}=\overline{ND}, let's denote this segments "k". On the other hand we have that \measuredangle~CBN=\measuredangle~BCN=45^\circ.

    Nevertheless, \triangle{ACB}\sim\triangle{BCD}\implies\overline{  BC}=k\sqrt2. Finally, \overline{BN}=\overline{CN}=k\implies\triangle{CDN  }~\text{is equilateral}, then \measuredangle~NDC=2x=60^\circ~\therefore~x=30^\ci  rc and the proof is completed.

    Post your problem now
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  6. #21
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    sweet! i like your approach!
    ok here's one of my favourite geometry problems. well actually i've changed it a bit, now it's a bit harder! if someone wants a hint i'll give them the original version... maybe.

    Let there be a rectangle that has a length that is twice the size of it's width, as shown in the diagram below.

    Prove x=60 degrees.
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  7. #22
    Senior Member OReilly's Avatar
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    Has anyone tried to solve this?

    I have tried many ideas, but failed.
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  8. #23
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    Prove that \overline{AB}=\overline{AC}
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  9. #24
    Senior Member OReilly's Avatar
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    Quote Originally Posted by Krizalid View Post


    Prove that \overline{AB}=\overline{AC}
    I had good idea, and tried many variants of it, but like I said I failed.

    If anyone wants I will post it, maybe someone will get new idea.
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  10. #25
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    I found another proof:


    • Take a point F on \overline{CD} such that \measuredangle~CBF=60^\circ\implies\overline{BF}=2  m~\therefore~\overline{AB}=\overline{BF}~\blacktri  angleleft
    • From \blacktriangleleft we have that \measuredangle~FAB=75^\circ\implies\triangle{ADF}\  cong\triangle{BCE}~\therefore~\overline{AF}=\overl  ine{BE}
    • Nevertheless, \overline{AB}\parallel\overline{EF}\implies\text{q  uadrilateral }ABEF~\text{isosceles trapezium} (and cyclic).
    • Finally x=\measuredangle~EAD=\measuredangle~FAD+\measureda  ngle~EAF=15^\circ+45^\circ=60^\circ and the proof is completed \blacksquare
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  11. #26
    Senior Member OReilly's Avatar
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    Nice proof.
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  12. #27
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    very nice proof! i like it alot! my proof involved creating an equadrilateral triangle with one side being BE and overlaps triangle ABE. once again, very sweet approach.

    well, knock us out with another question. *shudders* i'm scared of what your hard questions are like... scared and intrigued.
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  13. #28
    Senior Member DivideBy0's Avatar
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    Quote Originally Posted by blurgh View Post
    correction, my proof does use similar triangles. i found a mistake in my proof and had to fix it. (hehe, oops)
    um, i haven't got the hang of Latex, so i hope you don't mind if i give you a link to a pdf file instead. (you'll have to download it, sorry!)
    although i think and am more fluent in English, i always solve math problems in Vietnamese, so my proof is basically a literal translation of what i would've written in Vietnamese, so I'm sorry if it doesn't make sense in some parts. All symbols are what the Vietnamese use in our math, if there is anything different from what most people would write please tell me.
    once again, sorry for making you download a pdf file.


    my proof
    Wow, how were you able to make it so neat? A special program?
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  14. #29
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    Quote Originally Posted by blurgh View Post
    very nice proof! i like it alot! my proof involved creating an equadrilateral triangle with one side being BE and overlaps triangle ABE. once again, very sweet approach.

    well, knock us out with another question. *shudders* i'm scared of what your hard questions are like... scared and intrigued.
    Can you post your proof?
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  15. #30
    Math Engineering Student
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    Here's my problem



    Not so hard but it's a beautiful problem
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