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.

Question

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.

jhonyy9 · Answer

little down on your question - so if you check it - i have do it one picture please you write there if is this right,correct

anonymous · Answer

Use coordinate geometry

anonymous · Answer

Take A=(0,0) B=(a,0) C=(a,a) D=(0,a)
Use this only if you have given up for planar geometry

anonymous · Answer

Olympiad again?

anonymous · Answer

IMO 1974!

anonymous · Answer

I actually wanted to post it in the math olympiad group.But I am its only member!

anonymous · Answer

http://assets.openstudy.com/updates/attachments/4f2e3ef3e4b0571e9cbacadb-squeespleen-1328435401174-dodec.png

anonymous · Answer

Where AL is intersected by Bl it is bisected

anonymous · Answer

You are reading form this ( http://www.scribd.com/dorh7343/d/23254911-Mathematical-Olympiad-Challenges) book isn't ?

anonymous · Answer

yes

anonymous · Answer

It has solutions isn't?

anonymous · Answer

yes it does;but I want a pure geometric proof.

anonymous · Answer

Hm good luck :)