How should the radius MP be drawn?

[Hauserman]

I need help with this one.

The coloured parts space is limited by three semicircle archs of which the smaller has the radius r.

How should the radius MP be drawn, if you want it to divide the coloured space into two parts with
equally big areas?

 

[galactus]

See here for a nice explanation:

http://www.mathhelpforum.com/math-help/ ... drawn.html