Question

Find the area of triangle so formed in a circle of radius 40cm, if angle subtended by the chord at the centre of the circle is 120$°$

Answer 1

$$\begin{gathered} \text{A}\mathrm{rea}\mathrm{of}\mathrm{the}\mathrm{triangle}\mathrm{formed}\mathrm{by}\mathrm{two}\mathrm{radi}\text{i}\mathrm{and}\mathrm{chord} \\ =\frac{1}{2}\times {\mathrm{r}}^2\times \mathrm{sin\theta } \\ \text{H}\mathrm{ere},\mathrm{r}=\mathrm{radius}\mathrm{of}\mathrm{circle} \\ \mathrm{And}\mathrm{\theta }=\mathrm{central}\mathrm{angle} \\ \mathrm{Therefore},\text{a}\mathrm{rea}=\frac{1}{2}\times {\left(40\right)}^2\times \sin \left(120°\right) \\ =\frac{1}{2}\times 1600\times \frac{\sqrt{3}}{2} \\ =400\sqrt{3}{\mathrm{cm}}^2 \end{gathered}$$