document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1155987>Question 1155987</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A circle is inscribed into a right triangle. The point of tangency divides the hypotenuse in two segments with lengths 2 and 3. Find the radius of the circle </SPAN>\n" );
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document.write( "Let the triangle be ABC, with right angle at C.<br><BR>\n" );
document.write( "Let P, Q, and R be the points of tangency of the circle with sides AB, BC, and CA, respectively.<br><BR>\n" );
document.write( "We are given that AP=2 and PB=3.<br><BR>\n" );
document.write( "Two tangents from an external point to a circle are congruent, so RC=2 and QB=3.<br><BR>\n" );
document.write( "If r is the radius of the circle, then AC = 2+r and BC = 3+r.<br><BR>\n" );
document.write( "Then in triangle ABC,<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2Br%29%5E2%2B%283%2Br%29%5E2+=+5%5E2 ALIGN=MIDDLE  ALT=\"%282%2Br%29%5E2%2B%283%2Br%29%5E2+=+5%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "That equation is easily solved to find the radius.<br><BR>\n" );
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