SOLUTION: Chord AB and CD intersect each other at O inside the circle. AO = 8cm, CO= 12 cm, and DO = 20 cm. If AB is the diameter of the circle, compute the area of OCA.

We will calculate the area of sector APC, then calculate the area of ΔCOP 
and subtract it from the sector and that will leave the area of OCA.  
Go here:

http://www.algebra.com/tutors/students/your-answer.mpl?question=1189421

where I have already calculated ∠APC = 0.6290064738 radians.  The formula 
for a sector is  where θ is in radians.  

So the area of the sector APC is



Now we'll find the area of ΔCOP by Heron's formula:

}

where s represents the semi-perimeter.

The perimeter = CO+OP+CP = 12+11+19 = 42

The semi-perimeter is half of that or s = 21.

} 

}

} 

}

Subtracting the area of ΔCOP from the area of the
sector APC, we get

} cm2.

 Edwin