# Circumscribed circle

**Geometry**Level 4

A triangle \(ABC\) is circumscribed by a circle with center \(O\) . The arcs \( AB , BC \) and \( AC \) subtend the angles \(\alpha , \beta\) and \(\gamma\) respectively at \(O\) .

If the area of the circle is \(50\pi\) square units and that of the triangle is \(15\) square units , find the value of \(\sin\alpha + \sin\beta + \sin\gamma\) .

Give your answer correct to 3 significant figures.