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- 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.

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- anonymous

- jamiebookeater

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- anonymous

u have a picture?

- Directrix

Wondering where the points K, M, and N are located?

- jhonyy9

yes one picture may be importantly --- i think

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- Directrix

Click on "Draw" and sketch it , please.

- anonymous

L is an arbitrary point?

- anonymous

I think you forgot a triangle BCL

- jhonyy9

|dw:1328433505949:dw|

- jhonyy9

so this is like there this ?

- anonymous

I think it's something like this.

- anonymous

I'll try to solve this.

- 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

Inside... :( I'm horrible with English.
I'll make a new draw.

- anonymous

Now it's correct?

- anonymous

yes

- anonymous

We can Prove Angles are equal all of them it is very easy onlt the figure is complicated

- anonymous

Distances neednot be found

- anonymous

I have a proof using complex numbers but I want a purely geometric proof.

- anonymous

I'm wanting to use trigonometry :p, that's why I'm using distances to figure out the angles.

- 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

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

Label all points and I shall show you

- 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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