Question

Pe cercul de centru O si raza R=12 cm se iau doua pct A si B.Determinati lungimea coardei [AB],daca:
a)m(<AOB)=60 grade
b)m(<AOB)=120 grade 
c)d(O,AB)=8 cm
d)Aaob=36√3 cm²
e)m(arc AB)=90 grade

Answer 1

Faci figura si duci OM perp.pe AB
a)In tr OMA m<AOM=30, deci AM=$\frac{1}{2}$=6(am aplicat T < de 30 grade) AB=12
b) m<AOM=60gr. sin 60=$\frac{AM}{OA}$
AM=OA sin 60=$\frac{12\sqrt{3}}{2}=6 \sqrt{3} , \\ AB= 12 \sqrt{3}$
c)Aplic T lui Pitagora in tr AOM
$AM^{2}= 12^{2} - 8^{2}= 80 \\ AM=4 \sqrt5} \\ AB=8 \sqrt5}$
d)$36 \sqrt{3} = \frac{12.12sin\ \textless \ AOM}{2} \\ sin\ \textless \ AOM= \frac{ \sqrt{3} }{2} \\ m\ \textless \ AOM=60 \\ sin \ \textless \ AOM= \frac{AM}{12}= \frac{ \sqrt{3} }{2} \\ AM=6 \sqrt{3}, AB=12 \sqrt{3}$
e)m<AOB=90, $AB=AO \sqrt{2} =12 \sqrt{2}$