Question 1208874
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For simplicity (and without loss of generality), we may think that AB = 2,  
so the radius of the greatest circle is 1.


Then the radius of the intermediate circle is  {{{5/7}}}  and  its area is  {{{pi*(5/7)^2}}} = {{{pi*(25/49)}}};

     the radius of the smallest     circle is  {{{2/7}}}  and  its area is  {{{pi*(2/7)^2}}} = {{{pi*(4/49)}}}.


     The area of the greatest circle is  {{{pi*1^2}}} = {{{pi}}}.


The shaded area is  {{{pi}}} - {{{pi*(25/49)}}} - {{{pi*(4/49)}}} = {{{pi*(20/49)}}}.


The fraction of the shaded area is  {{{(pi*(20/49))/pi}}} = {{{20/49}}}.    <U>ANSWER</U>
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Solved.