The hardest easy geometry problem.

Discussion in 'General Off-Topic Chat' started by Veho, Dec 12, 2007.

Dec 12, 2007
  1. Veho
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    Global Moderator Veho The man who cried "Ni".

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    [​IMG]

    Find the value of x, with mathematical proof. No advanced trigonometry allowed. No algebra needed. Here's all you need to know:

    Lines and Angles: When two lines intersect, opposite angles are equal and the sum of adjacent angles is 180 degrees. When two parallel lines are intersected by a third line, the corresponding angles of the two intersections are equal.

    Triangles: The sum of the interior angles of a triangle is 180 degrees. An isosceles triangle has two equal sides and the two angles opposite those sides are equal. An equilateral triangle has all sides equal and all angles equal. A right triangle has one angle equal to 90 degrees. Two triangles are called similar if they have the same angles (same shape). Two triangles are called congruent if they have the same angles and the same sides (same shape and size).

    * Side-Angle-Side (SAS): Two triangles are congruent if a pair of corresponding sides and the included angle are equal.
    * Side-Side-Side (SSS): Two triangles are congruent if their corresponding sides are equal.
    * Angle-Side-Angle (ASA): Two triangles are congruent if a pair of corresponding angles and the included side are equal.
    * Angle-Angle (AA): Two triangles are similar if a pair of corresponding angles are equal.


    Remember, the answer must be in a form of an answer.

    Have fun going insane.
    [​IMG]








    [​IMG]
     


  2. rhyguy

    Member rhyguy GBAtemp Maniac

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    its less than 50:P
     
  3. xcalibur

    Member xcalibur Gbatemp's Chocolate Bear

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    easy,
    for this triangle, lets name the middle point x

    angle AXB is 50 degrees 180 - 130 = 50
    that makes AXD 130 because 180 - 50 = 130
    BXE is 130 also and DXE is 50

    angle XBE is 30 degrees to make triangle BXE a full 180 degrees
    triangle BDE is a right angled triangle so that makes angle BDE 90 degrees
    so that means 50 + 90 = 140 and that makes and DEB (x) = 40

    my geometry is a bit rusty so this might be completely wrong
     
  4. Veho
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    Global Moderator Veho The man who cried "Ni".

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    Wrong. XBE is 20, says so on the picture.
     
  5. xcalibur

    Member xcalibur Gbatemp's Chocolate Bear

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    I meant angle XEB
    I'm sorry, when you do something longwinded you tend to get lost.
    try doing trigonometric identities... those are loooooooong
     
  6. Veho
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    Global Moderator Veho The man who cried "Ni".

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    Okay, but it's still not it.

    Why do you think BDE is 90°? It looks like it, but there's no way to know that for sure.
     
  7. CockroachMan

    Member CockroachMan Scribbling around GBATemp's kitchen.

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  8. Veho
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    Global Moderator Veho The man who cried "Ni".

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    Prove it. Yeah, I know it's supposed to be 20°, but how do you get there? I need the procedure.

    EDIT:

    A picture drawn to scale.

    [​IMG]

    BDE is 110°.
     
  9. xcalibur

    Member xcalibur Gbatemp's Chocolate Bear

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    DAMNIT... i was hoping i wouldnt have to round it the loong way but i guess ill have to now :'(
    serves me for trying to take a shortcut

    angle ACB is 20
    angle BDC is 140
    angle ADX is 40
    angle AEB is 50

    and thats where im stuck...
    i cant seem to figure our trianle CDE and i need to go now...

    EDIT: i saw your post so i can get it now
    BDE is 110
    DXE is 50
    that makes DEX 110 +50 = 160
    180 - 160 = 20

    howd you get BDE?
     
  10. kellyan95

    Banned kellyan95 Banned

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    Print -> use protractor
     
  11. xcalibur

    Member xcalibur Gbatemp's Chocolate Bear

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    not to scale

    EDIT: i guess it is...
    that was a useless post
     
  12. Veho
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    Global Moderator Veho The man who cried "Ni".

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    Um... [​IMG]

    I don't know. I can't prove it. I know it's 110, and x=20°, but I can only prove it graphically, and this problem asks for discrete proof.
     
  13. shakirmoledina

    Member shakirmoledina Legend

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    Some unknown angles are known but if cockroachman could explain how he got 20...
    ADB = 40... AEb = 30.... EPB and DPA are 130 where P is central point and APB and DPE are 50
     
  14. CockroachMan

    Member CockroachMan Scribbling around GBATemp's kitchen.

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    don't know how to prove it.. [​IMG]

    for some reason, the triangles B-Center-E and DCE are equal.. but I can't remember why now.. something to do with the lines crossing them.. [​IMG]

    been some time since I've done this kind of thing..
     
  15. shakirmoledina

    Member shakirmoledina Legend

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    umm just a note that here we dont use AAS since
    * Angle-Side-Angle (AAs)
    * Angle-Angle (AA)
    as u can see above if 2 angles are equal why do u need to prove the side
     
  16. FrEEz902

    Member FrEEz902 GBAtemp Regular

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    Easy,

    X=60 degrees

    I'll scan my paper of ugly handwriting now

    Edit: Oh wait, i screwed something up >_
     
  17. TGBoy

    Member TGBoy GBAtemp Regular

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    I have seen this before. Isnt this the World's Hardest Easy Geometry Problem.

    The answer is 20.
    I seen the solution to it.
     
  18. ZAFDeltaForce

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  19. moozxy

    Member moozxy hamboning

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  20. FrEEz902

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