document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1191626>Question 1191626</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The tangent PT to a circle touches the circle at P. If the radius of the circle is 2.8cm and OT is 5.5cm, calculate the length of the tangent </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #823409 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=823409\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> OP is equal to 2.8 cm.<BR>\n" );
document.write( "OT is equal to 5.5.<BR>\n" );
document.write( "right triangle OPT is formed with OT as the  hypotenuse and OP as one of the legs.<BR>\n" );
document.write( "PT is the other leg, which is also the tangent line to the circle.<BR>\n" );
document.write( "OPT is the right angle.<BR>\n" );
document.write( "let OP = x and PT = y and OT = z.<BR>\n" );
document.write( "by pythagorus, z^2 = x^2 + y^2<BR>\n" );
document.write( "replace x with 2.8 because that's the length of OP, and replace z with 5.5 because that's the length of OT, and you get 2.8^2 + y^2 = 5.5^2.<BR>\n" );
document.write( "solve for y^2 to get y^2 = 5.5^2 - 2.8^2 = 22.41.<BR>\n" );
document.write( "solve for y to get y = sqrt(22.41) = 4.733920151.<BR>\n" );
document.write( "that's the length of PT which is the tangent.<BR>\n" );
document.write( "that should be your answer.<BR>\n" );
document.write( "you can say it's sqrt(22.41) or you can say it's 4.733920151.<BR>\n" );
document.write( "you can round 4.733920151 as required, if that's the way  they want to see the answer.<BR>\n" );
document.write( "the answer depends on the fact that the tangent to a circle is perpendicular to the radius of the circle at the point of tangency.<BR>\n" );
document.write( "here's a reference on tangent to a circle.<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.cuemath.com/geometry/tangent/\" target = \"_blank\">https://www.cuemath.com/geometry/tangent/</a><BR>\n" );
document.write( "let me know if you have any questions or concerns.<BR>\n" );
document.write( "theo\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
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