document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1101149>Question 1101149</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A circle with centre O has a radius of 8 cm, from O to T. Segment AT is tangent to the circle. X is a point on AT. Y is the point where XO intersects the circle. Angle AOT=60 degrees, and AX=XY (this length is labelled as m). Find the length of m. </SPAN>\n" );
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document.write( "With angle AOT 60 degrees, triangle AOT is a 30-60-90 right triangle.<br><BR>\n" );
document.write( "OT is the radius of the circle, which is 8; so AT is 8*sqrt(3) and AO is 16.<br><BR>\n" );
document.write( "AX=XY=m; so TX = 8*sqrt(3)-m and XO = 8+m.<br><BR>\n" );
document.write( "Then in right triangle TOX we have<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64+%2B+192+-+16sqrt%283%29m+%2B+m%5E2+=+m%5E2+%2B+16m+%2B+64 ALIGN=MIDDLE  ALT=\"64+%2B+192+-+16sqrt%283%29m+%2B+m%5E2+=+m%5E2+%2B+16m+%2B+64\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12+-+sqrt%283%29m+=+m ALIGN=MIDDLE  ALT=\"12+-+sqrt%283%29m+=+m\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12+=+m%28sqrt%283%29%2B1%29 ALIGN=MIDDLE  ALT=\"12+=+m%28sqrt%283%29%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+12%2F%28sqrt%283%29%2B1%29+=+%2812%28sqrt%283%29-1%29%29%2F%28%28sqrt%283%29%2B1%29%28sqrt%283%29-1%29%29+=+%2812%28sqrt%283%29-1%29%29%2F2+=+6%28sqrt%283%29-1%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );