document.write( "Question 452537: The circles are concentric. The inner circle is shaded. The cord is tangent to the inner circle and has length 12. What is the area of the non-shaded region? \n" ); document.write( "
Algebra.Com's Answer #311073 by pedjajov(51)\"\" \"About 
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When you draw a picture you get that tangent touches inner circle and intersects with the outer circle.
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\n" ); document.write( "Area of non shaded area is a difference between areas of outer and inner circle.
\n" ); document.write( "If radius of inner circle is r1 and radius of outer circle is r2 we have:
\n" ); document.write( "\"Ai=r1%5E2%2AP\", where P is Pi.
\n" ); document.write( "\"Ao=r2%5E2%2AP\"
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\n" ); document.write( "So non shaded are is:
\n" ); document.write( "\"A=Ao-Ai=%28r2%5E2-r1%5E2%29%2AP\"\r
\n" ); document.write( "\n" ); document.write( "We have three points:
\n" ); document.write( "- point C for center of the circle(s)
\n" ); document.write( "- point A where tangent touches inner circle
\n" ); document.write( "- point B where tangent intersects outer circle
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\n" ); document.write( "These three points connected form right triangle with legs CA and AB and hypotenuse CB.
\n" ); document.write( ":
\n" ); document.write( "Leg CA is radius for inner circle r1.
\n" ); document.write( "Hypotenuse CB is radius for outer circle r2.
\n" ); document.write( ":Point A also divides tangent exactly at half so AB is 6.
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\n" ); document.write( "Now we can form Pythagorean theorem for this triangle as:
\n" ); document.write( "\"r1%5E2%2B6%5E2=r2%5E2\"
\n" ); document.write( "\"r2%5E2-r1%5E2=36\"
\n" ); document.write( ":
\n" ); document.write( "If we replace this into formula for area A we have
\n" ); document.write( "\"A=36%2AP\" \n" ); document.write( "
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