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MathNet 2006 — Part 04 Question 100

Math Olympiad Vault · MathNet 2006 — Part 04

Question 100

Dana is a cube $A B C D E F G H$. On the page $G H$ lies the point $K$, so that holds $|G K|:|K H|=1:3$, on the page $H E$ lies the point $L$, so that holds $|H L|:|L E|=1:1$, on the page $C G$ so there lies the point $M$. What should be the relationship $|C M|:|M G|$, so that they will move $A K$ in $L M$ once?