a)
notam AB=a BC=b AC=BD=c AO=OB=DO=OC=c/2
P(AOB)=50 ⇒ a+c=50
P(BOC)=36 ⇒ b+c=36
P(ABC)=60 ⇒ a+b+c=60
a+b+c+c=86 ⇒c=86-60=26 cm ⇒ BC=b=36-26=10 cm AB=a=50-26=24 cm
b)
A(ABCD)=24×10=240 cm²
c)
A(BOC)=240/4=60 cm²
ducem BM _I_OC
A(BOC)=OC×BM/2 =26/2=13 cm
60=13×BM/2
BM=2×60/13=120/13
sin (∡BOC)= (120/13)/13=120/169
