document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199419>Question 1199419</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 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<BR>\n" );
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document.write( "https://ibb.co/6bcN9jh\r<BR>\n" );
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document.write( "A) 160<BR>\n" );
document.write( "B) 215<BR>\n" );
document.write( "C) 245<BR>\n" );
document.write( "D) 260<BR>\n" );
document.write( "E) 280<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #833303 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=833303\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "The tutor @ikleyn has the right idea.<BR>\n" );
document.write( "However, she made a slight typo.<BR>\n" );
document.write( "Side AB should be 5*sqrt(3) cm long.<BR>\n" );
document.write( "Edit: Ignore this paragraph as she has corrected the error.\r<BR>\n" );
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document.write( "For any 30-60-90 triangle, we have this template<BR>\n" );
document.write( "short leg = x<BR>\n" );
document.write( "long leg = x*sqrt(3)<BR>\n" );
document.write( "hypotenuse = 2x\r<BR>\n" );
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document.write( "In this case x = 5<BR>\n" );
document.write( "The short leg of this template is always opposite the 30 degree angle. <BR>\n" );
document.write( "Smallest side opposite the smallest angle.\r<BR>\n" );
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document.write( "Since AB = 5*sqrt(3) and BC = 5, it leads to triangle ABC having an area of (25/2)*sqrt(3) square cm. <BR>\n" );
document.write( "I skipped the steps so let me know if you need to see them.\r<BR>\n" );
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document.write( "Then solving the equation<BR>\n" );
document.write( "(1/2)*r*10 = (25/2)*sqrt(3)<BR>\n" );
document.write( "will lead to<BR>\n" );
document.write( "r = (5/2)*sqrt(3)\r<BR>\n" );
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document.write( "area of the full circle = pi*r^2<BR>\n" );
document.write( "area of quarter circle = (1/4)*pi*r^2<BR>\n" );
document.write( "area of quarter circle = (1/4)*pi*( (5/2)*sqrt(3) )^2<BR>\n" );
document.write( "area of quarter circle = (75/16)pi<BR>\n" );
document.write( "area of quarter circle = 4.6875pi<BR>\n" );
document.write( "area of quarter circle = 4.6875*3.14<BR>\n" );
document.write( "area of quarter circle = 14.71875<BR>\n" );
document.write( "The value is approximate because pi = 3.14 is approximate.\r<BR>\n" );
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document.write( "Unfortunately none of the answer choices you posted are close to this value. <BR>\n" );
document.write( "It's possible your teacher made a typo, or you might have mixed up problems/answer choices by mistake. <BR>\n" );
document.write( "Please revise carefully.<BR>\n" );
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