Question

Pe cercul de centru O si raza R=12 cm se iau 2 puncte A si B.Determinati lungimea cordei [AB],daca: a) m (AOB)=60° b)m (AOB)=120° c) d(O,AB)=8 cm d) A AOB=36radical 3 cm patrati e) m (AB)=90°

Answer 1

OM⊥AB

a)

m(∡AOM)=30°

AM=1/2=6 ( aici am teorema de 30 ° )

AM=12 cm

b)

m(∡AOM)=60°

sin60°=AM/OA⇒
⇒√3/2=12/OA ⇒
⇒OA=12*√3/2 ⇒
⇒OA=6√3cm

AB=12√3cm

c)

Teorema lui Pitagora in ΔAOM dr in O  ⇔

⇔ i²=c1²+c2² ⇔
⇔AM²=12²-8² ⇔
⇔AM²=144-64=80 ⇔
⇔AM=√80 ⇔
⇔AM=4√5 cm

AB=8√5 cm

sin(∡AOM)=√3/2

d)

m(∡AOM)=60°

sin(∡AOM)=AM/12=√3/2⇔

⇔ AM=12√3/2⇔
⇔AM=6√3cm

AB=12√3cm

e)

m(∡AOB)=90°

AB=AO√2 = 12√2 cm

Sper ca te am ajutat!!!!