document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=809979>Question 809979</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the center and radius of the circle circumscribed about the right triangle with vertices (1,1), (1,4) and (7,4). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #487891 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=487891\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The segment connecting (1,1) and (1,4) is part of the vertical line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The segment connecting (1,4) and (7,4) is part of the horizontal line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=4 ALIGN=MIDDLE  ALT=\"y=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Obviously those are the legs of the right triangle,<BR>\n" );
document.write( "the right angle is at point (1,4),<BR>\n" );
document.write( "and the segment connecting (1,1) and (7,4) is the hypotenuse.\r<BR>\n" );
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document.write( "THE CENTER:<BR>\n" );
document.write( "If you are studying circles, maybe you were taught that an angle inscribed in a circle measures half of the central angle that subtends the same arc.<BR>\n" );
document.write( "Maybe you were told that the corollary is that the intercepted arc on an inscribed right angle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180%5Eo ALIGN=MIDDLE  ALT=\"180%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > and that makes the corresponding chord a diameter.<BR>\n" );
document.write( "In that case, you would realize that the the hypotenuse of the triangle is the diameter and its midpoint is the center of the circle.<BR>\n" );
document.write( " <BR>\n" );
document.write( "If you are studying triangles, maybe you were taught that all three perpendicular bisectors of a the sides of a triangle intersect at the circumcenter, the center of the circumscribed circle.<BR>\n" );
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document.write( "Either way, you find the coordinates of the center as the midpoint of the hypotenuse, or as the intersection of the horizontal and vertical perpendicular bisectors doing the calculations<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5BC%5D=%281%2B7%29%2F2=8%2F2=4 ALIGN=MIDDLE  ALT=\"x%5BC%5D=%281%2B7%29%2F2=8%2F2=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5BC%5D=%281%2B4%29%2F2=5%2F2=2.5 ALIGN=MIDDLE  ALT=\"y%5BC%5D=%281%2B4%29%2F2=5%2F2=2.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-1%2C9%2C-3%2C7%2C%0D%0Agrid%281%29%2C%0D%0Acircle%284%2C2.5%2C3sqrt%285%29%2F2%29%2C%0D%0Acircle%284%2C2.5%2C0.1%29%2Cred%28circle%281%2C1%2C0.2%29%29%2C%0D%0Ared%28circle%281%2C4%2C0.2%29%29%2Cred%28circle%287%2C4%2C0.2%29%29%2C%0D%0Ablue%28line%281%2C1%2C1%2C4%29%29%2C%0D%0Ablue%28line%281%2C4%2C7%2C4%29%29%2C%0D%0Ablue%28line%281%2C1%2C7%2C4%29%29%2C%0D%0Agreen%28line%28-1%2C2.5%2C9%2C2.5%29%29%2C%0D%0Agreen%28line%284%2C7%2C4%2C-3%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "THE RADIUS:<BR>\n" );
document.write( "The radius is half of the diameter.<BR>\n" );
document.write( "The diameter is the segment connecting (1,1) and (7,4),<BR>\n" );
document.write( "and you can calculate its length as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%287-1%29%5E2%2B%284-1%29%5E2%29=sqrt%286%5E2%2B3%5E2%29=sqrt%2836%2B9%29=sqrt%2845%29=sqrt%289%2A5%29=sqrt%289%29%2Asqrt%285%29=3sqrt%285%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the radius is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%283sqrt%285%29%2F2%29 ALIGN=MIDDLE  ALT=\"highlight%283sqrt%285%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = approximately<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3.354%29 ALIGN=MIDDLE  ALT=\"3.354%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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