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Gheorghe Țițeica 2025 Grade 8 P3
AndreiVila   1
N 19 minutes ago by sunken rock
Source: Gheorghe Țițeica 2025
Two regular pentagons $ABCDE$ and $AEKPL$ are given in space, such that $\angle DAC = 60^{\circ}$. Let $M$, $N$ and $S$ be the midpoints of $AE$, $CD$ and $EK$. Prove that:
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[*] $\triangle NMS$ is a right triangle;
[*] planes $(ACK)$ and $(BAL)$ are perpendicular.
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Ukraine Olympiad
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AndreiVila
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sunken rock
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