document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1158588>Question 1158588</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The segments GA and GB are tangent to a circle at A and B, and AGB is a 60-degree<BR>\n" );
document.write( "angle. Given that GA = 12 cm, find the distance from G to the nearest point on 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 #781776 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=781776\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Let C be the center of the circle; let P be the point of intersection  of CG and the circle.<br><BR>\n" );
document.write( "The shortest distance from G to a point on the circle is the length of GP.<br><BR>\n" );
document.write( "Angle AGB is 60 degrees, so angle AGC is 30 degrees.<br><BR>\n" );
document.write( "Then triangle AGC is a 30-60-90 right triangle.<br><BR>\n" );
document.write( "AG=12 means AC=6 and CG=6*sqrt(3).<br><BR>\n" );
document.write( "CP is also 6; that makes GP 6*sqrt(3)-6.<br><BR>\n" );
document.write( "ANSWER: 6*sqrt(3)-6<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );