Wednesday, February 18, 2009

Problem 13: Triangle, Angles, Congruence, Cevian

Proposed Problem
Problem 13: Triangle, Angles, Congruence.

See complete Problem 13 at:
http://gogeometry.com/problem/problem013.htm

Level: High School, SAT Prep, College geometry

Post your solutions or ideas in the comments.

8 comments:

  1. Solucion:
    http://forogeometras.com/index.php?topic=884.0
    http://img25.imageshack.us/img25/7149/rsolmarzo8.jpg

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  2. trazar DE//AB
    el angulo EDC=4x
    Los triangulos ABD y DCE son congruentes
    entonces ABD=3x
    en el triangulo ABC: 3x+4x+3x+5x=180
    x=12º

    atte:tino!!!

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  3. Dear Tino,
    The answer is not correct.
    Why triangles ABD and DCE are congruent?

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  4. We've CD/sin(5x)=BC/sin(8x) and AB/sin(3x)=BC/sin(4x). Thus, sin(5x)/sin(8x)=sin(3x)/sin(4x) or
    sin(5x)/2sin(4x)cos(4x)=sin(3x)/sin(4x) or
    sin(5x)/2cos(4x)=sin(3x)
    By inspection if x=10 then sin(5x)=cos(4x) and sin(3x)=1/2. Thus, x=10 is clearly a solution to the equation.
    Ajit: ajitathle@gmail.com

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  5. This comment has been removed by a blog administrator.

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  6. http://ahmetelmas.files.wordpress.com/2010/05/cozumlu-ornekler.pdf

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  7. Solution by cristian, my partnert >:)

    http://youtu.be/neHBBXZiaRI

    Go Go Geometry!

    Geo-Greetings ^^!

    ReplyDelete
  8. https://www.youtube.com/watch?v=-i4RlIl4B0s

    ReplyDelete