08 Circles with diameters equal to corresponding sides of the triangle

Problem
From the figure shown below, O1, O2, and O3 are centers of circles located at the midpoints of the sides of the triangle ABC. The sides of ABC are diameters of the respective circles. Prove that
 

$A_1 + A_2 + A_3 = A_4$

 

where A1, A2, A3, and A4 are areas in shaded regions.
 

Circles with centers at midpoints of sides of a right triangle

 

Solution

 
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