Question

Pe cercul O si raza R=18 cm se iau 2 pct distincte A si B. Determinati masura arcului mic AB daca aria OAB = 81 cm patrati?

Answer 1

[tex]A_{\Delta AOB}=\dfrac{AO\cdot OB\cdot \sin(\ \textless \ AOB)}{2}=\dfrac{R^2\cdot sin(\ \textless \ AOB)}{2}\\ \text{Prin urmare:}\\ \dfrac{R^2\cdot \sin(\ \textless \ AOB)}{2}=81\\ 324\cdot \sin(\ \textless \ AOB)=162\\ \sin(\ \textless \ AOB)=\dfrac{1}{2}\Rightarrow m(\ \textless \ AOB)=30\textdegree\\ m(\overarc{AB})= m(\ \textless \ AOB)=30\textdegree[/tex]