Hello, Kevin!

Draw radius downward, perpendicular to

Let

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: .

Hence: .

Therefore, we must draw radius so that angle