document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1150432>Question 1150432</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two circles are tangent to each other at A and the centre of the larger circle is at C. The lines AB and FC are perpendicular diameters of the larger circle. If BD = 9 cm and FE = 5 cm, then what is the radius of the smaller circle, in centimeters?<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 #771831 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=771831\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The statement of the problem is faulty; but the intent is clear.  FC is a radius, not a diameter; let G be the point on the large circle that makes FG a diameter.<br><BR>\n" );
document.write( "Let H be the other point of intersection of the small circle with diameter FG.<br><BR>\n" );
document.write( "Let x be the length of segment CD.<br><BR>\n" );
document.write( "Since BD = 9, the radius of the large circle is x+9.  In particular, AC = 9<br><BR>\n" );
document.write( "Since EF = 5, CE = CH = x+4..<br><BR>\n" );
document.write( "AD and EH are chords of the small circle, intersecting at C.  From the theorem about the lengths of the pieces of two intersecting chords in a circle,<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x%2B9%29+=+%28x%2B4%29%28x%2B4%29 ALIGN=MIDDLE  ALT=\"x%28x%2B9%29+=+%28x%2B4%29%28x%2B4%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%2B9x+=+x%5E2%2B8x%2B16 ALIGN=MIDDLE  ALT=\"x%5E2%2B9x+=+x%5E2%2B8x%2B16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+16 ALIGN=MIDDLE  ALT=\"x+=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The diameter of the small circle is x + (x+9) = 2x+9 = 41.<br><BR>\n" );
document.write( "So the radius of the small circle is 20.5.<br>\r<BR>\n" );
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