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Patrulater circumscriptibil
Posted: Tue Jun 16, 2009 3:02 pm
by Mateescu Constantin
Daca \( I \) este centrul cercului inscris intr-un patrulater circumscriptibil \( ABCD \) de laturi \( AB=a,\ BC=b,\ CD=c,\ DA=d \), atunci \( IA\cdot IC+IB\cdot ID=\sqrt{abcd} \).
Posted: Tue Jun 16, 2009 4:31 pm
by Marius Mainea
Se foloseste faptul ca \( \frac{IA^2}{ad}+\frac{IB^2}{ab}=1. \)
De asemenea \( \frac{IA^2}{IC^2}=\frac{ad}{bc} \) si \( \frac{IB^2}{ID^2}=\frac{ab}{dc}. \)
Posted: Tue Jun 16, 2009 8:55 pm
by mihai miculita
Vezi teorema 10 de la pag. 16 din articolul lui Darij Grinberg:
http://www.cip.ifi.lmu.de/~grinberg/CircumRev.pdf