find area of darkened figure 
We know that length of diameter $AB=6$; $CA=2\sqrt{3}$; 
 We should find area of darkened figure I have tried  following :
Since $AB$ is diameter  we  can say $ACB$ is right triangle  so 

we can caluclate  area of $ABC$, but my question is how calculate   area  of this triangle inside circle? Please help me.

$\triangle ABC$ is half an equilateral triangle making $\angle BCA = \pi /3$ and $\angle CBA = \pi /6$, so if $D$ is the intersection of $BC$ and the circle then $\triangle OAD$ is equilateral, and with the circle radius of 3 you can calculate all the areas.   
