document.write( "Question 1206037: Hello! Here is my question. I'm really having a hard time solving it and tried answering it many times. I don't know if how am I going to get it.\r
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\n" ); document.write( "Cecile from Philippines \n" ); document.write( "
Algebra.Com's Answer #843230 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "I'm going to guess what your problem is.  I'll bet there are two concentric\r\n" );
document.write( "circles, the smaller circle has a radius of OP = 6 cm. Chord AB is tangent to\r\n" );
document.write( "the smaller circle at P. And AB = \"12sqrt%283%29\"cm.  Find the area of the \r\n" );
document.write( "shaded region, the shaded segment of the larger circle.  Isn't that what\r\n" );
document.write( "you want?\r\n" );
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document.write( "Draw the two radii OA and OB of the larger circle (in red):\r\n" );
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document.write( "\"PA=expr%281%2F2%29AB=expr%281%2F2%29%2A12sqrt%283%29=6sqrt%283%29\"\r\n" );
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document.write( "Use the Pythagorean theorem on right triangle OPA.\r\n" );
document.write( "\"OA%5E2=OP%5E2%2BPA%5E2\"\r\n" );
document.write( "\"OA%5E2=6%5E2%2B%286sqrt%283%29%29%5E2\"\r\n" );
document.write( "\"OA%5E2=36%2B36%2A3\"\r\n" );
document.write( "\"OA%5E2=36%2B108\"\r\n" );
document.write( "\"OA%5E2=144\"\r\n" );
document.write( "\"OA=sqrt%28144%29\"\r\n" );
document.write( "\"OA=12\" = radius of larger circle.\r\n" );
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document.write( "Triangle OPA is a 30-60-90 right triangle because its shortest side OP=6 cm\r\n" );
document.write( "and its longest side OA, is 12, twice the shortest side.\r\n" );
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document.write( "So angle AOP = 60o = π/3 radians, and angle AOB = 120o = 2π/3 radians.\r\n" );
document.write( "We find the area of the sector OAB and subtract the area of triangle OAB.\r\n" );
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document.write( "Area of the sector is \r\n" );
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document.write( "Area of triangle AOP = \"expr%281%2F2%29%2AAP%2APB=expr%281%2F2%29%2A6%2A6%2Asqrt%283%29=18sqrt%283%29\"\r\n" );
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document.write( "Area of triangle AOB = twice area of AOP = \"36sqrt%283%29\"\r\n" );
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document.write( "Subtract the area of the triangle from the area of the sector:\r\n" );
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document.write( "\"48pi-36sqrt%283%29\"\"%22%22=%22%22\"\"12%284pi-3sqrt%283%29%29\"\r\n" );
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document.write( "About 88.4 cm2.\r\n" );
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document.write( "Edwin

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