document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1189759>Question 1189759</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A circle with area 1369ℼ cm^2 passes through A and B, and is tangent to line CD. If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%2Fy+=+1%2F3+ ALIGN=MIDDLE  ALT=\"+x%2Fy+=+1%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, find y in cm.\r<BR>\n" );
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document.write( "Diagram: https://imgur.com/gox1hfD (I tried my best to draw in the circle) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #821224 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=821224\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "With an area of 1369ℼ, the radius of the circle is 37.<br><BR>\n" );
document.write( "Let O be the center of the circle; let E be the point where the segment with length y in the diagram intersects CD; and let F be the point of tangency of the circle with line CD.  Draw the diameter FG, intersecting AB at H.<br><BR>\n" );
document.write( "The diameter FG is the perpendicular bisector of chord AB, so the length of GB is x/2.  The given information <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Fy=1%2F3 ALIGN=MIDDLE  ALT=\"x%2Fy=1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > then tells us that EB/GB=6.  So<br><BR>\n" );
document.write( "Let GB = w<BR>\n" );
document.write( "Then BE = 6w<br><BR>\n" );
document.write( "Draw radius OB and look at right triangle OHB.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28OH%29%5E2%2Bw%5E2=37%5E2 ALIGN=MIDDLE  ALT=\"%28OH%29%5E2%2Bw%5E2=37%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=OH=sqrt%281369-w%5E2%29 ALIGN=MIDDLE  ALT=\"OH=sqrt%281369-w%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Then we can see FH=EB=6w, so<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=37%2Bsqrt%281369-w%5E2%29=6w ALIGN=MIDDLE  ALT=\"37%2Bsqrt%281369-w%5E2%29=6w\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%281369-w%5E2%29=6w-37 ALIGN=MIDDLE  ALT=\"sqrt%281369-w%5E2%29=6w-37\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1369-w%5E2=%286w-37%29%5E2 ALIGN=MIDDLE  ALT=\"1369-w%5E2=%286w-37%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=1369-w%5E2=36w%5E2-444x%2B1369 ALIGN=MIDDLE  ALT=\"1369-w%5E2=36w%5E2-444x%2B1369\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=37w%5E2-444w=0 ALIGN=MIDDLE  ALT=\"37w%5E2-444w=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=37w%28w-12%29=0 ALIGN=MIDDLE  ALT=\"37w%28w-12%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=12 ALIGN=MIDDLE  ALT=\"w=12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "y is the length of EB, which is 6w = 72.<br><BR>\n" );
document.write( "ANSWER: y = 72 cm<br><BR>\n" );
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