Răspuns:
a)36cm
Explicație pas cu pas:
AB=diametru=>OA=OB=raze=6cm=>AB=12cm
O=mij. AB=>Fie OC mediana;dar
ΔABC isoscel(AC=BC) =>CO=inaltime,bisectoare=>m(∡OCA)=m(∡OCB) si m(∡COA)=m(∡COB)=90°;
C∈cerc=>OC raza=>OC=OB=>ΔOCB isoscel=>m(∡OCB)=m(∡OBC)=(180°-90°):2=45°
m(∡ACB)=m(∡ACO)+m(∡BCO)=45°+45°=90°
In ΔCOB dreptunghic:
OC=OB=6cm
=>t.pit. OB²+OC²=CB²=>36cm²+36cm²=BC²=>
BC²=102cm²=>BC=6√2cm
In ΔABC dr ∡C:
Aria= (c1×c2):2=(AC×BC):2=(6√2×6√2):2=36√4:2=36cm²
Sper ca te am ajutat!<3
