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OJM Dambovita 2011 Subiectul 4

 
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Andi Brojbeanu
Newton


Joined: 22 Mar 2009
Posts: 383
Location: Targoviste (Dambovita)

PostPosted: Sun Apr 03, 2011 7:16 pm    Post subject: OJM Dambovita 2011 Subiectul 4 Reply with quote

a) Demonstrati ca intr-un triunghi isoscel unghiurile de la baza sunt congruente.
b) Se da triunghiul isoscel ABC, AB=AC, m(\angle{A})>90\textdegree. Se noteaza cu M punctul de intersectie dintre perpendiculara in A pe AC si perpendiculara in B pe BC, iar cu N punctul de intersectie dintre perpendiculara in A pe AB si perpendiculara in C pe BC. Daca {P}=BN \cap CM, demonstrati ca [AP este bisectoarea unghiului BAC.
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Brojbeanu Andi Gabriel, clasa XII-a
Colegiul National "Constantin Carabella" Targoviste
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