document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1133555>Question 1133555</A>: <I><SPAN STYLE=\"word-break: break-all;\"> AB is the diameter of a circle. AD and BC are tangents to the circle with AD=9 cm and BC=16 cm. If AC and BD intersect at a point on the circle, then what is the length of AB in cm?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #750984 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=750984\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "If AD and BC are tangents to a circle at the endpoints of diameter AB, and if AC and BD intersect at a point on the circle, then AD and BC are perpendicular to diameter AB and are on the same side of AB.<br><BR>\n" );
document.write( "Let E be the point of intersection of AC and BD; E is on the circle.  Let F be on AB with EF perpendicular to AB.<br><BR>\n" );
document.write( "Using similar triangles (or other methods) it can be determined that EF = (AD*BC)/(AD+BC) = 144/25.<br><BR>\n" );
document.write( "Also using similar triangles, it can be determined that AF:FB = 9:16.<br><BR>\n" );
document.write( "So let AF=9x anf FB=16x; then once again similar triangles tell us that<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AF%2FEF=EF%2FFB ALIGN=MIDDLE  ALT=\"AF%2FEF=EF%2FFB\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x%2F%28144%2F25%29=%28144%2F25%29%2F16x ALIGN=MIDDLE  ALT=\"9x%2F%28144%2F25%29=%28144%2F25%29%2F16x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=144x%5E2+=+%28144%2F25%29%5E2 ALIGN=MIDDLE  ALT=\"144x%5E2+=+%28144%2F25%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%5E2+=+144%2F625 ALIGN=MIDDLE  ALT=\"x%5E2+=+144%2F625\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+12%2F25 ALIGN=MIDDLE  ALT=\"x+=+12%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Then the length we are looking for, AB, is AF+FB = 25x = 12.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );