In the figure shown, arc ADB and arc BEC are semicircles, each with a radius of one unit. Point D, point e and point F are the midpoints of arc ADB, arc BEC and arc DFE, respectively. If arc is also a semicircle, what is the area of the shaded region?
+129852 EP's solution/approach are perfectly valid.....here's one more way....
Let M be the center of circle ADB
Draw DB
The area between chord DB and the arc DB is given by
[ pi/4 - 1/2 ] (1)
Using symmetry......the shaded area =
Area of circle containing arc DFE - 4 times (1) =
pi - 4 [ pi/4 - 1/2 ] =
pi - pi + 2 =
2 units^2
