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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?

 Nov 11, 2019
 #1
avatar+19913 
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With r = 1, I find the shaded area (in units2 ) as below:

 Nov 11, 2019
 #2
avatar+27 
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i tryed to post an image but it didnt work???????!!!!!!!!

 Nov 11, 2019
 #3
avatar+106533 
+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

 

cool cool cool

 Nov 11, 2019

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