Question

Fie A,B€C (O,10cm).Determinati lungimea coardei[AB],daca:

a)m(<AOB)=120º

b)d(O,AB)=6cm

c)m(AB)=90º

d)Aria lui AOB=25radical din3cm2

Answer 1

a)[tex]m(\widehat{AOB})=120 \Rightarrow m(\widehat{OAB})=m(\widehat{OBA})=30\\ \cos 30=\dfrac{\dfrac{AB}{2}}{10}=\dfrac{\sqrt{3}}{2} \Rightarrow AB=10\sqrt{3}[/tex]
b)$tg \; 30=\dfrac{6}{\dfrac{AB}{2}}=\dfrac{\sqrt{3}}{3} \Rightarrow AB=12\sqrt{3}$
c)$m(\widehat{AOB})=90 \Rightarrow AB=r\sqrt2 \Rightarrow AB=10\sqrt2$
d)[tex]\sin30=\dfrac{h}{10}=\dfrac{1}{2}\Rightarrow h=5\\ A_{\Delta AOB}=\dfrac{AB}{2}\cdot5=25\sqrt3\Rightarrow AB=10\sqrt3[/tex]