a. Aria triunghiului echilateral
[tex]A=\frac{l^2\sqrt{3} }{4}\\\\ A=\frac{12^2\sqrt{3} }{4} =\frac{144\sqrt{3} }{4} =36\sqrt{3} cm^2[/tex]
b. ∡ABC=60°⇒∡ABD=180-60=120°
BM bisectoare⇒∡MBN∡MBD=120:2=60°
MN║BD⇒ BM secanta ⇒∡NMB=∡MBD=60° (alterne interne)
In ΔMBN, avem 2∡ de 60°⇒∡BNM=60°⇒ΔMBN echilateral ⇒ΔABC~ΔMBN
