document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=759509>Question 759509</A>: <I><SPAN STYLE=\"word-break: break-all;\"> MATH QUESTION~\r<BR>\n" );
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document.write( "A wheel rests against a floor and a vertical wall. A point P on the rim of the wheel is 2cm and 9cm from the floor and wall respectively Calculate the radius of the wheel.\r<BR>\n" );
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document.write( "Please help!<BR>\n" );
document.write( "Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #462112 by </B><A HREF=/tutors/aboutme.mpl?userid=htmentor><B>htmentor(1343)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=htmentor><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=htmentor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=462112\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If the wheel is resting on the floor and against the wall, the tangent lines are x=0 and y=0 and the points of tangency are (r,0) and (0,r).  <BR>\n" );
document.write( "The equations for the lines perpendicular to these tangent lines at these points are x=r and y=r and they must go through the center of the circle.<BR>\n" );
document.write( "So the center of the circle is (r,r)<BR>\n" );
document.write( "The standard form for a circle is (x-a)^2 + (y-b)^2 = r^2 where (a,b) is the center and r is the radius<BR>\n" );
document.write( "Since the point P is 2 cm from the floor and 9 cm from the wall, the point is (9,2)<BR>\n" );
document.write( "Inserting the point (9,2) in the equation for the circle gives<BR>\n" );
document.write( "(9-r)^2 (2-r)^2 = r^2<BR>\n" );
document.write( "Simplify and solve for r:<BR>\n" );
document.write( "81 - 18r + r^2 + 4 - 4r + r^2 = r^2<BR>\n" );
document.write( "r^2 - 22r + 85 = 0<BR>\n" );
document.write( "This can be factored as <BR>\n" );
document.write( "(r-17)(r-5) = 0<BR>\n" );
document.write( "This gives two possible solutions, r=5 cm and r=17 cm<BR>\n" );
document.write( "The graph below shows the two circles which share the point (9,2)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+400%2C+400%2C+-4%2C+38%2C+-4%2C+38%2C%0D%0A++grid%28+1+%29%2C%0D%0A++red%28+circle%28+5%2C+5%2C+5+%29+%29%2C%0D%0A++blue%28+circle%289%2C+2%2C+0.3%29+%29%2C%0D%0A++green%28+circle%28+17%2C+17%2C+17+%29+%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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