Draw radius downward, perpendicular to
Ignore the two smaller semicircles for the moment.
If the shaded region is the semicircle , then bisects the area.
But a semicircle with area has been subtracted from quadrant
. . and added to quadrant
For the new area is to be bisected by radius ,
. . the area of sector must equal
The area of sector
So we have: .
Therefore, we must draw radius so that angle