anonymous
  • anonymous
Please help.I am confused! Inside a square ABCD construct the equilateral triangles ABK,CDM,and DAN.Prove that the midpoints of the segments KL,LM,MN,NK and those of AN,AK,BK,BL,CL,CM,DM, and DN are the vertices of a regular dodecagon.
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
u have a picture?
Directrix
  • Directrix
Wondering where the points K, M, and N are located?
jhonyy9
  • jhonyy9
yes one picture may be importantly --- i think

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Directrix
  • Directrix
Click on "Draw" and sketch it , please.
anonymous
  • anonymous
L is an arbitrary point?
anonymous
  • anonymous
I think you forgot a triangle BCL
jhonyy9
  • jhonyy9
|dw:1328433505949:dw|
jhonyy9
  • jhonyy9
so this is like there this ?
anonymous
  • anonymous
I think it's something like this.
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anonymous
  • anonymous
I'll try to solve this.
jhonyy9
  • jhonyy9
SqueeSpleen --- ATTENTION --- this exersice begin with the word ,,inside a square ..." - so i think that in this way your picture not can being right,correct how do you think ?
anonymous
  • anonymous
Inside... :( I'm horrible with English. I'll make a new draw.
anonymous
  • anonymous
Now it's correct?
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anonymous
  • anonymous
yes
anonymous
  • anonymous
We can Prove Angles are equal all of them it is very easy onlt the figure is complicated
anonymous
  • anonymous
Distances neednot be found
anonymous
  • anonymous
I have a proof using complex numbers but I want a purely geometric proof.
anonymous
  • anonymous
I'm wanting to use trigonometry :p, that's why I'm using distances to figure out the angles.
anonymous
  • anonymous
KM=(1-2(1-cos(30)))CB distance between mid point kn and midpoint nm=KM/2 I forget the parenthesis. the first time.
anonymous
  • anonymous
Take only two adjacent angle and try to proof them equal I have done it Then you can use symetry argument to extend it to all adjacent pairs
anonymous
  • anonymous
Label all points and I shall show you
anonymous
  • anonymous
I'm horrible with geometry but I'll label all points and left it to you. Geometry problems were the problems who gave me the worst times when I was in my countrys maths olympiads :( I named the mid points of the segments after their extrems.
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