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  • Hardest Easy Math Problem

    Click image for larger version  Name:	hardest-easy-geometry-thumb-social.png?w=600&ssl=1.png Views:	0 Size:	17.5 KB ID:	81073

  • #2
    hints ascending in their usefulness from top(very vague) to bottom(discreet):

    1 SPOILER the sum of all three angles in any triangle is always 180°!
    2 SPOILER calculate some angles! ;-)
    3 SPOILER usually in geometry the points of any shape are counted incremental A, B, C, ... always one next letter per increment.
    4 SPOILER one letter has been skipped! For a reason...
    5 SPOILER point D is missing and you have to create it to solve the problem!
    6 SPOILER between which letters is D in the alphabet?
    7 SPOILER create point D on the line between C and E
    8 SPOILER draw the line DB
    9 SPOILER consider the triangle DBC
    10 SPOILER D is not fix yet. Try to pick a place for D which is for your advantage
    11 SPOILER put D where DBC is a isosceles triangle (a triangle where two sides are of equal length and therefore has two equal angles)
    12 SPOILER angle BCD is 80°. Which angle do you need to set for CBD for CDB to equal BCD=80°?
    13 SPOILER set CBD=20° so that CDB=180°-80°-20°=80°=BCD. triangle BCD is now a isosceles triangle. lines BC and BD have the same length! BC=BD
    14 SPOILER try to find more isosceles triangles.
    15 SPOILER An isosceles triangle is a triangle where two sides are of equal length and therefore must have two equal angles. But vice versa it's also true that it is a triangle which has two equal angles and therefore must have two sides of equal length!
    16 SPOILER calculate the angle BFC
    17 SPOILER angle BFC=50°
    18 SPOILER since angle BFC=50° and angle BCF=50°, triangle BCF is an isosceles triangle! sides BC=BF
    19 SPOILER try to find even more isosceles triangles.
    20 SPOILER you need to create a line
    21 SPOILER draw the line DF
    22 SPOILER calculate angles DBF BDF and BFD
    23 SPOILER All angles in triangle BDF are 60°. triangle BDF is an equilateral triangle! All sides of this triangle have the same length! BD=BF=DF (=BC)
    24 SPOILER analyse triangle BDE
    25 SPOILER triangle BDE is also an isosceles triangle! DB=DE (=BC=BF=DF)
    26 SPOILER now analyse triangle DEF
    27 SPOILER since DE=DF, triangle DEF is also an isosceles triangle.
    28 SPOILER angle DFE = angle DEF
    29 SPOILER DFE=70°=DEF
    30 SPOILER x=DEF-40°=30°

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    • #3
      Langley's Adventitious Angles is a mathematical problem posed by Edward Mann Langley in the journal The Mathematical Gazette in 1922.
      Chinese paper describing geometric solution of anonymous "Ms. aerile_re" in 2015 translated to English
      "This work solves the first of the three unsolved problems listed by Rigby in his 1978 paper [of the journal The Mathematical Gazette]"
      Last edited by Linkblade; 03-27-2020, 12:03 PM.

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      • #4
        an excerpt of the 2015 geometric solution (wtf...):
        Click image for larger version  Name:	3circumcenter_d20180609 - PDF-XChange Editor_2020-03-27_13-04-13.jpg Views:	0 Size:	73.2 KB ID:	81120
        Last edited by Linkblade; 04-02-2020, 09:26 AM.

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