The figure shows circle O with diameter AB and inscribed angle ABC with AB = 8 and BC = 4. When the area of the shaded region, in square units, is expressed in the form a + bπ, what is the value of ab?
Draw a line from point O to point C.
Because OB and OC are radii, OB = BC = OC = 4. Therefore, we know that triangle OBC is an equilateral triangle. Solving for the area of OBC gives us 4sqrt(3).
In addition, since we know that Angle COA is 120 degrees(as angle BOC is 60), the rest of the area would be 1/3 of the area of the whole circle. This is 16/3pi.
Hence, the area of the shaded region is: 4sqrt(3) + 16/3pi
ab = 64sqrt(3)/3