document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1146408>Question 1146408</A>: <I><SPAN STYLE=\"word-break: break-all;\">  The radii of two circular pulleys with their centers 10 cm apart are 3 cm and 4 cm, respectively. They are interconnected by a cross-belt so that they rotate in opposite direction. Find the distance between two points of tangency of the two different circles measured along the belt.  </SPAN>\n" );
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document.write( "The problem in 2 dimensions is to find the length of an internal tangent to two circles with radii 3cm and 4cm whose centers are 10cm apart.  There is a standard method for solving this general problem.<br><BR>\n" );
document.write( "Draw the figure with the two circles, the line segment connecting the centers of the two circles, and an internal tangent.<BR>\n" );
document.write( "Draw the radii of the two circles to the points of tangency.<BR>\n" );
document.write( "Using the radius of the small circle and the internal tangent as two sides, form a rectangle by extending the radius of the large circle by an amount equal to the radius of the small circle.  Then draw the fourth side of that rectangle.<br><BR>\n" );
document.write( "You now have a right triangle in which the hypotenuse is the distance between the centers of the two circles (10cm) and one leg has a length equal to the sum of the radii of the two circles (7cm).<br><BR>\n" );
document.write( "The length of the other leg is the length of the internal tangent.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+=+10%5E-7%5E2+=+51 ALIGN=MIDDLE  ALT=\"x%5E2+=+10%5E-7%5E2+=+51\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+sqrt%2851%29 ALIGN=MIDDLE  ALT=\"x+=+sqrt%2851%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: The distance between the points of tangency of the belt with the two pulleys, measured along the belt, is sqrt(51) cm. </SPAN>\n" );
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