# Circumscribed circle

Geometry Level 3

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 $$\sin\alpha + \sin\beta + \sin\gamma$$ .