fie ΔABC si M,N,P mijloacele laturilor AB, BC, CA
fie AQ⊥BC
dem ca MQNP e trapez isoscel
M mijlocul lat AB si P mijl lat AC => MP linie mijl => MP|| BC=> MP||QN
=> MQNP trapez
N mijl lat BC si P mijl lat AC => PN linie mijl => PN=1/2 AB=BM
in ΔBQA dr in A avem QM=1/2 AB=BM (ca raze in cercul circumscris ΔABQ dr in Q)
=>PN=BM=MQ => trapezul MQNP este isoscel
O seara buna!
