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MathNet 2010 — Part 04 Question 126

Math Olympiad Vault · MathNet 2010 — Part 04

Question 126

They $A B C D$ A trapezium with $A B \| C D$, $2|A B|=|C D|$ and $B D \perp B C$. They $M$ the middle of $C D$ and they $E$ The intersection of $B C$ and $A D$. They $O$ The intersection of $A M$ and $B D$. They $N$ The intersection of $O E$ and $A B$.


a. Prove that $A B M D$ is a window.


b. Prove the line $D N$ through the middle of the line segment $B E$ goes.