Triangle in circle

The vertices of the triangle ABC lie on a circle with a radius 3, which is divided into three parts in the ratio 4:4:4.

Calculate the circumference of the triangle ABC.

Final Answer:

o =  15.6

Step-by-step explanation:

$$\begin{gathered} {\Phi }_1=360\cdot \frac{4}{4+4+4}=120^{\circ } \\ {\Phi }_2=360\cdot \frac{4}{4+4+4}=120^{\circ } \\ {\Phi }_3=360\cdot \frac{4}{4+4+4}=120^{\circ } \\ a=2\cdot 3\cdot \sin \frac{{\Phi }_1}{2}=5.2 \\ b=2\cdot 3\cdot \sin \frac{{\Phi }_2}{2}=5.2 \\ c=2\cdot 3\cdot \sin \frac{{\Phi }_3}{2}=5.2 \\ o=a+b+c=15.6 \end{gathered}$$

Try another example