document.write( "Question 1199419: In the diagram, line BC = 5 cm, and curved line DE is tangent to line AC. Find the area, in cm2, of the quarter circle BDE with centre B.\r
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\n" ); document.write( "\n" ); document.write( "A) 160
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Algebra.Com's Answer #833302 by ikleyn(52790)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "How you formulate the problem in your post,  it makes me cry:
\n" ); document.write( "so mathematically illiterate the formulation is.\r
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\n" ); document.write( "\n" ); document.write( "Therefore, I will edit it to present it in a decent shape.\r
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document.write( "    In the diagram, ABC is a right triangle with the right angle at B.\r\n" );
document.write( "    Angle C is 30°. The leg BC is 5 cm long. \r\n" );
document.write( "    Circular arc DE with the center at B is tangent to hypotenuse AC. \r\n" );
document.write( "    Find the area, in cm2, of the quarter circle BDE.\r\n" );
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\n" ); document.write( "\n" ); document.write( "                Next, the solution by @josgarithmetic is incorrect,\r
\n" ); document.write( "\n" ); document.write( "                starting from the second line of his post. \r
\n" ); document.write( "\n" ); document.write( "                AB is not 10 cm, as he mistakenly states in his post.\r
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\n" ); document.write( "\n" ); document.write( "                Therefore, ignore his solution,  since it is wrong.\r
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\n" ); document.write( "\n" ); document.write( "                I came to bring you a correct solution.\r
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document.write( "Since the angle A is 30°, the hypotenuse AC is 10 cm and the leg AB is  10*cos(30°) = \"10%2A%28sqrt%283%29%2F2%29\" = \"%285%2Asqrt%283%29%29\".\r\n" );
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document.write( "Then the area of the triangle ABC is  \"%281%2F2%29%2Aabs%28BC%29%2Aabs%28AC%29\" = \"%281%2F2%29%2A%285%2A%285%2Asqrt%283%29%29%29%29\" = \"%2825%2Asqrt%283%29%29%2F2\".\r\n" );
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document.write( "Next, the radius of the circle \"r\" is the height of the triangle ABC, drawn from vertex B to the hypotenuse AC.\r\n" );
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document.write( "Therefore, the area of the triangle ABC in other form can be presented as  \"%281%2F2%29%2Ar%2A10\"  cm^2.\r\n" );
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document.write( "The area is the same, so we can write this equation\r\n" );
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document.write( "    \"%281%2F2%29%2Ar%2A10\" = \"%2825%2Asqrt%283%29%29%2F2\"  cm^2.\r\n" );
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document.write( "It gives\r\n" );
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document.write( "          r    = \"%285%2A%28sqrt%283%29%29%2F2%29\"  cm.\r\n" );
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document.write( "Now the area of the quarter of the circle is\r\n" );
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document.write( "    \"%28pi%2Ar%5E2%29%2F4\" = \"%28pi%2A25%2A3%29%2F%284%2A4%29%29\" = \"%283.14%2A75%29%2F16\" = 14.72  cm^2  (rounded).    ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "No one of the listed numbers in your post is not even close to the right answer.\r
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\n" ); document.write( "\n" ); document.write( "It is easy to see, without making long calculations, that all listed numbers in your post are not even close to the right answer.\r
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\n" ); document.write( "\n" ); document.write( "Indeed, the radius of the circle is, obviously, shorter than 5 cm.\r
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\n" ); document.write( "\n" ); document.write( "Hence, the area of the quarter of the circle  MUST  be less than   \"%28pi%2Ar%5E2%29%2F4\" = \"%283.14%2A5%5E2%29%2F4\" = 19.625 cm^2.\r
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\n" ); document.write( "\n" ); document.write( "Compare it with your numbers.\r
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\n" ); document.write( "\n" ); document.write( "                Then  REPORT  to  YOUR  PROFESSOR  that all your \r
\n" ); document.write( "\n" ); document.write( "                attached answers  ARE  INCORRECT  NUMBERS.\r
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