document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=737118>Question 737118</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A large circle of radius 1 is drawn tangent to perpendicular rays. Find the radius of the biggest possible circle that is placed in the space. (The smaller circle must also be tangent to the perpendicular rays. )\r<BR>\n" );
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document.write( "Show all work and give an exact answer - no rounding at any time, and no decimals.\r<BR>\n" );
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document.write( "Remember: the radius of the small circle does not include the space between the small circle and the right angle formed by the perpendicular rays.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #450193 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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/cgi-bin/show-face.mpl?user=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=450193\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A large circle of radius 1 is drawn tangent to perpendicular rays. Find the radius of the biggest possible circle that is placed in the space.<BR>\n" );
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document.write( "You didn't make it clear, but I think you mean a smaller circle tangent to the 2 rays and tangent to the larger circle.<BR>\n" );
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document.write( "Use the x & y axes<BR>\n" );
document.write( "The larger circle is (x-1)^2 + (y-1)^2 = 1<BR>\n" );
document.write( "The tangent point (call it T) on both circles is (1 - sqrt(2)/2,1 - sqrt(2)/2) [apx (0.2928,0.2928)]<BR>\n" );
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document.write( "The center of the small circle is equidistant from T, the x-axis and the y-axis.<BR>\n" );
document.write( "For T at (x,y):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+y+=+sqrt%28%28x+-+1+%2B+sqrt%281%2F2%29%29%5E2+%2B+%28y+-+1+%2B+sqrt%281%2F2%29%29%5E2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since x = y<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+sqrt%28%28x+-+1+%2B+sqrt%281%2F2%29%29%5E2+%2B+%28x+-+1+%2B+sqrt%281%2F2%29%29%5E2%29 ALIGN=MIDDLE  ALT=\"x+=+sqrt%28%28x+-+1+%2B+sqrt%281%2F2%29%29%5E2+%2B+%28x+-+1+%2B+sqrt%281%2F2%29%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+sqrt%282%28x+-+1+%2B+sqrt%281%2F2%29%29%29%5E2 ALIGN=MIDDLE  ALT=\"x+=+sqrt%282%28x+-+1+%2B+sqrt%281%2F2%29%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+sqrt%282%2A%28x%5E2+%2B+1+%2B+2x%2Asqrt%281%2F2%29+-+2sqrt%281%2F2%29+%2B+1%2F2%29%29 ALIGN=MIDDLE  ALT=\"x+=+sqrt%282%2A%28x%5E2+%2B+1+%2B+2x%2Asqrt%281%2F2%29+-+2sqrt%281%2F2%29+%2B+1%2F2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > *** I left out a term of -2x<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+=+2%2A%28x%5E2+%2B+2x%2Asqrt%281%2F2%29+-+2sqrt%281%2F2%29+%2B+3%2F2%29 ALIGN=MIDDLE  ALT=\"x%5E2+=+2%2A%28x%5E2+%2B+2x%2Asqrt%281%2F2%29+-+2sqrt%281%2F2%29+%2B+3%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+=+2x%5E2+%2B+4x%2Asqrt%281%2F2%29+-+4sqrt%281%2F2%29+%2B+3 ALIGN=MIDDLE  ALT=\"x%5E2+=+2x%5E2+%2B+4x%2Asqrt%281%2F2%29+-+4sqrt%281%2F2%29+%2B+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+%284x+-+4%29%2Asqrt%281%2F2%29+%2B+3+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+%284x+-+4%29%2Asqrt%281%2F2%29+%2B+3+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+x%2Asqrt%288%29+-+sqrt%288%29+%2B+3+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+x%2Asqrt%288%29+-+sqrt%288%29+%2B+3+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------<BR>\n" );
document.write( "Now it's a quadratic.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-sqrt%282%29+%2B+sqrt%28%288+-+4%2A%283+-+sqrt%288%29%29%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+-sqrt%282%29+%2B+sqrt%28%288+-+4%2A%283+-+sqrt%288%29%29%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-sqrt%282%29+%2B+sqrt%288+-+12+%2B+4sqrt%288%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+-sqrt%282%29+%2B+sqrt%288+-+12+%2B+4sqrt%288%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-sqrt%282%29+%2B+sqrt%284sqrt%288%29+-+4%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+-sqrt%282%29+%2B+sqrt%284sqrt%288%29+-+4%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-sqrt%282%29+%2B+sqrt%28sqrt%288%29+-+1%29 ALIGN=MIDDLE  ALT=\"x+=+-sqrt%282%29+%2B+sqrt%28sqrt%288%29+-+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "A mistake somewhere, see if you can find it.\r<BR>\n" );
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document.write( "I'll finish it later, but this is how it's done. </SPAN>\n" );
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