Thursday, December 31, 2009

Problem 411: Triangle, Median, Angles

Proposed Problem
Click the figure below to see the complete problem 411 about Triangle, Median, Angles.

Problem 411: Triangle, Median, Angles.
See also:
Complete Problem 411
Level: High School, SAT Prep, College geometry

Posted by Antonio Gutierrez at 3:58 PM
Labels: , ,

10 comments:

  1. AnonymousDecember 31, 2009 at 5:40 PM

    http://geometri-problemleri.blogspot.com/2009/12/problem-59-ve-cozumu.html

    ReplyDelete
  2. c .t . e. oJanuary 1, 2010 at 2:33 AM

    draw DE middle line of ABC

    DE = X = 1/2 AC = 6

    ReplyDelete
  3. mugremJanuary 29, 2010 at 1:39 PM

    simular triangles x=6

    ReplyDelete
  4. AnonymousMarch 23, 2010 at 5:14 AM

    x = 5.443

    ReplyDelete
  5. Antonio GutierrezMarch 23, 2010 at 6:26 AM

    To Anonymous, March 23, 2010 5:14 AM

    x = 5.443 (Not correct)

    ReplyDelete
  6. baeOctober 18, 2010 at 7:06 AM

    Hint : 51+51+78 = 180

    ReplyDelete
  7. AnonymousDecember 6, 2010 at 4:02 AM

    I'm korean, i am interested in your math problems,,
    i solved it that way : straight AC so DA parallel ED.. and triangle BEA is isosceles triangle,, finally 1:2=x:12 x=6 am i right?
    i'm sorry i can't write english well,,

    ReplyDelete
  8. Antonio GutierrezDecember 6, 2010 at 5:24 AM

    To Anonymous, problem #411: Your answer is right (I think that in your solution: DA is parallel to BE)

    ReplyDelete
  9. APOSTOLIS MANOLOUDISJune 17, 2016 at 1:46 PM

    Problem 411
    In extension of the CA to get A point E such that EA=AD=x ,so triangle BAD= triangle BAE(<EAB=<BAD=51) then BE=BD and <EBA=<ABC, so BE/BC=EA/AC or ½=x/12
    Therefore x=6.

    ReplyDelete
  10. GregMay 28, 2022 at 5:56 AM

    A graphical solution
    See diagram here
    Rotating ΔABD clockwise by π around D we get ΔA’B’D such that (ADA^' ) ̂ = π and B’ = C so that polygon ADA’B’C is equal to ΔAA’C
    In ΔAA’C, (AA^' C) ̂ = (DA^' C) ̂ = (DAB) ̂ = 51° and (ACA^' ) ̂= 180° - 78° - 51° = 51°
    Therefore ΔAA’C is isosceles in A and AA’ = 2.x = AC
    Hence x = 6
    QED

    ReplyDelete

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