Răspuns:
Explicație pas cu pas:
m(AB)/3=m(AC)/4=m(BC)/5=k⇒m( arc(AB))=3k,m (arc (AC))=4k;m(arc(BC))=5k dar
12k=360°⇒k=30°
deci m(arc(AB))=3·30=90°;m(arc(AC))=4·30=120°;m(arc(BC))=5·30=150°
⇒m(A)=75°:m(∡(B))=60°;m(∡C))=45°
m(arc(AC))=60°⇒ latura L3=R√3=12√2·√3=12√6 cm⇒AC=12√6 cm:
m(arc(AB))=90°⇒latura L4=R√2=12√2·√2=12·2 cm⇒AB=24 cm:..
L3,L4 reprezinta laturile unui Δechilateral,respectiv a unui patrat inscrise intr- un cerc...
in ΔdrADC cos 45°=PD/AC⇒PD=AC sin 45°=12√6 √2/2= 12√3 cm;
in Δdr ADB sin 30°=BD/AB⇒AB=BD/sin 30°=24·1/2=12 cm
BC=12√3+12=12(√3+1)cm
Perimetrul P=12(3+√3+√6)cm;
b)EF=?
m(arc(FCE))=m(arc(AC))+m(arc(CE))=60°+90°=150°⇒FE≡BC=12(√3+1) cm
