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?

Guest Nov 11, 2019

#3**+1 **

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

CPhill Nov 11, 2019