Explicație pas cu pas:
500<n<1000
n:15=c1r=5=>n=15c1+5=>n-5=15c1
n:18=c2r=5=>n=18c2+5=>n-5=18c2
n:24=c3r=5=>n=24c3+5=>n-5=24c3
Deci avem ca:
n-5=15c1=> 15|n-5
n-5=18c2=>18|n-5
n-5=24c3=>24|n-5
Inseamna ca n-5 :[15,18,24] =>
n-5:360 => n-5€{360,720,1080..} dar cum
500<n<100 => n-5=720 => n=725
a)mABD=mDAC=>2mABD=mBAC=>
2mABD+mABD+30=180 =>3mABD=150 => mABD=50 => mBAC=100
b)mBAC=100 =>mDAC=50
mDAC+30+mADC=180=>80+mADC=180 =>mADC=100
DE bisectoare ADC=>mADE=50 dar cum mBAD=50 si AD secanta =>AB||DE
c)mDAB=mDBA=>Triunghiul ABD isoscel =>BD=AD
mADE=mDAE(50) => Triunghiul ADE isoscel => DE=AE
BD+DE=AD+AE=>AD+AE=AD+AE Adevarat
