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60^o angle wanted, equilateral on a square
parmenides51   4
N 6 minutes ago by MathIQ.
Source: 2019 Austrian Mathematical Olympiad Junior Regional Competition , Problem 2
A square $ABCD$ is given. Over the side $BC$ draw an equilateral triangle $BCS$ on the outside. The midpoint of the segment $AS$ is $N$ and the midpoint of the side $CD$ is $H$. Prove that $\angle NHC = 60^o$.
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(Karl Czakler)
4 replies
parmenides51
Dec 18, 2020
MathIQ.
6 minutes ago
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Geometry inmo problem
Enes040612   2
N Apr 25, 2025 by Red_gear5246
Source: INMO 2008
Can anyone help with this problem? the book also starts the solution by saying IA1=IB1=IC1=2r which I'm not understanding why. The problem is at the attachments.
2 replies
Enes040612
Feb 13, 2025
Red_gear5246
Apr 25, 2025
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Geometry inmo problem
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Source: INMO 2008
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Enes040612
4 posts
Enes040612
#1 h  Feb 13, 2025, 8:10 AM
Y by
Can anyone help with this problem? the book also starts the solution by saying IA1=IB1=IC1=2r which I'm not understanding why. The problem is at the attachments.
Attachments:
Z K Y
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CHESSR1DER
69 posts
CHESSR1DER
#2 h  Feb 13, 2025, 9:20 AM
Y by
Let $IA1 \cap BC = H$. Then since $IH = r$ and $IH = A1H$, then $IA1= 2r$. Other are similar.
This post has been edited 2 times. Last edited by CHESSR1DER, Feb 13, 2025, 9:21 AM
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Red_gear5246
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Red_gear5246
#3 h  Apr 25, 2025, 1:29 PM
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@Enes040612 which book are u solving?
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