Convex angle

There is a circle k (S; r), and a point A, which lies on this circle. There is also a point B on the circumference, for which it is true that in one direction, it is five times further from point A than in the opposite direction (around the circumference of the circle). Find the magnitude of the BSA convex angle.

Final Answer:

BSA =  60 °

Step-by-step explanation:

$$\begin{gathered} o_1=2\cdot \pi \cdot r\cdot \alpha /360 \\ {o}_2=2\cdot \pi \cdot r\cdot \beta /360 \\ o=o_1+o_2 \\ 2\cdot \pi \cdot r=2\cdot \pi \cdot r\cdot \alpha /360+2\cdot \pi \cdot r\cdot \beta /360 \\ 1=\alpha /360+\beta /360 \\ 360=\alpha +\beta \\ {o}_2=5\cdot o_1 \\ x+y=360{}^{\circ } \\ y=5\cdot x \\ x+5\cdot x=360 \\ 6x=360 \\ x=\frac{360}{6}=60 \\ x=60 \\ BSA=\angle BSA=x=60=60^{\circ } \end{gathered}$$

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