document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=636584>Question 636584</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let P be a point inside a square S so that the distances from P to the four vertices, in order, are 7, 35, 49, and x.  What is x? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #401456 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=401456\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 636584<BR>\n" );
document.write( "Let P be a point inside a square S so that the distances from P to the four vertices, in order, are 7, 35, 49, and x.  What is x?<BR>\n" );
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document.write( "Make the square's vertices at (0,0), (0,s), (s,s) and (s,0)<BR>\n" );
document.write( "The square is s by s units<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "P is 7 units from (0,0), 35 units from (0,s) and 49 units from (s,s)<BR>\n" );
document.write( "P is the intersection of 3 circles with the vertices as centers and the radii as given.<BR>\n" );
document.write( "----------<BR>\n" );
document.write( "The circles are:<BR>\n" );
document.write( "x^2 + y^2 = 49<BR>\n" );
document.write( "(x-s)^2 + y^2 = 1225<BR>\n" );
document.write( "(x-s)^2 + (y-s)^2 = 2401<BR>\n" );
document.write( "Solve for s<BR>\n" );
document.write( "-------<BR>\n" );
document.write( "(x-s)^2 + y^2 = 1225<BR>\n" );
document.write( "(x-s)^2 + (y-s)^2 = 2401<BR>\n" );
document.write( "--------------------------- Subtract<BR>\n" );
document.write( "(y-s)^2 - y^2 = 1176<BR>\n" );
document.write( "-2sy + s^2 = 1176<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "=============<BR>\n" );
document.write( "x^2 + y^2 = 49<BR>\n" );
document.write( "(x-s)^2 + y^2 = 1225<BR>\n" );
document.write( "--------------------------- Subtract<BR>\n" );
document.write( "x^2 - (x-s)^2 = - 1176<BR>\n" );
document.write( "2sx - s^2 = -1176<BR>\n" );
document.write( "s^2 - 2sx = 1176<BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "==================<BR>\n" );
document.write( "x^2 + y^2 = 49<BR>\n" );
document.write( "(x-s)^2 + (y-s)^2 = 2401<BR>\n" );
document.write( "--------------------------- Subtract<BR>\n" );
document.write( "-2sx + s^2 - 2sy + s^2 = 2352<BR>\n" );
document.write( "s^2 - sx - sy = 1176<BR>\n" );
document.write( "===================================<BR>\n" );
document.write( "I'll finish this later.<BR>\n" );
document.write( "If you want to see it, email via the Thank You note. <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );