document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=756225>Question 756225</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A square of area 40 cm2 is inscribed in a semicircle.\r<BR>\n" );
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document.write( "Find the area of the square that could be inscribed in a circle of the same radius. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #460051 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=460051\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I solved only halfway through, enough to get the radius and equation of the circle.\r<BR>\n" );
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document.write( "This would go better with a picture, but that was easier on paper than arranging it for the posting of a solution.\r<BR>\n" );
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document.write( "The inscribed square is 40 sq. units, so each side is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Asqrt%2810%29 ALIGN=MIDDLE  ALT=\"2%2Asqrt%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Using a graph with diameter of semicircle on x axis, the middle of the diameter on the origin, the semicirlce above the x axis;<BR>\n" );
document.write( "Lower side is from -x to x.  Left and right sides each are length y and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2%2Asqrt%2810%29 ALIGN=MIDDLE  ALT=\"y=2%2Asqrt%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Because we have a square figure, we can find on the graph, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=sqrt%2810%29 ALIGN=MIDDLE  ALT=\"x=sqrt%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "EQUATION for CIRCLE is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2=r%5E2 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2=r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and we wish to know r  the radius.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%2810%29%29%5E2%2B%282%2Asqrt%2810%29%29%5E2=r%5E2 ALIGN=MIDDLE  ALT=\"%28sqrt%2810%29%29%5E2%2B%282%2Asqrt%2810%29%29%5E2=r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50=r%5E2 ALIGN=MIDDLE  ALT=\"50=r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28r=5%2Asqrt%2810%29%29 ALIGN=MIDDLE  ALT=\"highlight%28r=5%2Asqrt%2810%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > the radius.\r<BR>\n" );
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document.write( "That is as I say, only halfway through to your finished solution, meaning only halfway solved.  Can you take the rest of the way?  At least you know the radius of the circle and its equation.\r<BR>\n" );
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document.write( "TO CONTINUE, here is a big hint.  <BR>\n" );
document.write( "The square inscribed in circle, NOT simply the semi-circle, will have the same center as that of the circle.  Since square, there are four triangles formed with the central angle of 90 degrees.  RIGHT Triangles, each of them.  Two sides of 5*sqrt(10).  This is a special triangle. The 90-45-45 type.  Height and base each are same measure as the radius of the circle and there are four of these triangles.\r<BR>\n" );
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document.write( "Area is (1/2){base}{height} and done four times.<BR>\n" );
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document.write( "Final answer should be 125 square units.  See how? </SPAN>\n" );
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