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MathNet 2006 — Part 04 Question 37

Math Olympiad Vault · MathNet 2006 — Part 04

Question 37

Sia $ABCD$ a quadrilateral; chiamiamo $E$ the intersezione (different from $A$) after the diameter circle $AB$ and $AC$ ed $F$ the intersezione (always different from $A$) after the diameter circle $AC$ and $AD$. I will show that:


a. is $E\widehat{A}D = 90^\circ$ and $BC$ is parallel to $AD$


b. is $E\widehat{A}D = F\widehat{A}B = 90^\circ$ and $ABCD$ is a parallelogram


c. is $ABCD$ is a parallelogram to $E\widehat{A}D = F\widehat{A}B = 90^\circ$.