document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1148362>Question 1148362</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In the diagram to the bottom, circle with center O has a radius of 8cm. Segment AT is tangent to the circle. Angle AOT=60 degrees, and AX=XY (this length is labeled m). Find the length of m. \r<BR>\n" );
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document.write( "Diagram: https://imgur.com/a/5jS4WF7 </SPAN>\n" );
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document.write( "With angle AOT 60 degrees and the radius OT=8, we can conclude that AO=16 and AT=8*sqrt(3).<br><BR>\n" );
document.write( "Then in right triangle XOT we have legs XT=8*sqrt(3)-m and OT=8, and hypotenuse XO=8+m.  So<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%5E2%2B%288%2Asqrt%283%29-m%29%5E2+=+%288%2Bm%29%5E2 ALIGN=MIDDLE  ALT=\"8%5E2%2B%288%2Asqrt%283%29-m%29%5E2+=+%288%2Bm%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Solving that equation, the m^2 terms on the two sides cancel, leaving a linear equation in m, making it possible to find an exact value for m (in radical form).<br><BR>\n" );
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