Conditie ca un triunghi sa fie isoscel

Claudiu Mindrila · Post by **Claudiu Mindrila** » Wed Jul 08, 2009 4:18 pm

Fie \( M \) mijlocul laturii \( BC \) a unui triunghi \( ABC \). Notam cu \( I \) si \( J \) centrele cercurilor inscrise in triunghiurile \( ABM \), respectiv \( ACM \). Daca \( m\left(\widehat{AIB}\right)-m\left(\widehat{MIJ}\right)=90^{\circ} \), sa se demonstreze ca \( \left[AB\right]\equiv\left[AC\right] \).

Florian Dumitrel, Marius Perianu

Marius Mainea · Post by **Marius Mainea** » Thu Jul 09, 2009 11:07 am

\( m\left(\widehat{AIB}\right)-m\left(\widehat{MIJ}\right)=90^{\circ} \) \( \Longrightarrow \) \( IJ\parallel BC \) \( \Longrightarrow \) \( \left[AB\right]\equiv\left[AC\right] \)