document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=704781>Question 704781</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An isosceles triangle ABC has it vertices on a circle. If line(AB) =13cm, line(BC) =13cm and line(AC) = 10cm. Calculate the radius of the circle to the nearest whole cm. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #434407 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=434407\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-9%2C9%2C-9%2C9%2C%0D%0Acircle%280%2C0%2C7.042%29%2Ctriangle%280%2C7.042%2C-5%2C-4.958%2C5%2C-4.958%29%2C%0D%0Agreen%28line%280%2C7.042%2C0%2C-4.958%29%29%2Cgreen%28rectangle%280%2C-4.958%2C+0.4%2C-4.558%29%29%2C%0D%0Ablue%28line%280%2C0%2C2.5%2C1.042%29%29%2Clocate%28-5.5%2C-5%2CA%29%2C%0D%0Alocate%285.1%2C-5%2CB%29%2C+locate%28-0.2%2C7.8%2CC%29%2Clocate%28-0.2%2C-5%2CF%29%2C%0D%0Alocate%282.7%2C1.7%2CD%29%2Clocate%28-0.7%2C0.5%2CE%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > CF is the altitude to base AB and part of AB's perpendicular bisector.<BR>\n" );
document.write( "DE is part of BC's perpendicular bisector. (CDE is a right angle).<BR>\n" );
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document.write( "All points in a perpendicular bisector are equidistant from the ends of the segment.<BR>\n" );
document.write( "Being on the perpendicular bisectos of AB and BC,<BR>\n" );
document.write( "point E is at the same distance from A, B, and C,<BR>\n" );
document.write( "so it is the center of the circle.<BR>\n" );
document.write( "EC is the radius of the circle.<BR>\n" );
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document.write( "AB=10, AF=FB=10/2=5, BC=13, BD=CD=13/2=6.5<BR>\n" );
document.write( "Using the Pythagorean theorem,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=CF=sqrt%2813%5E2-5%5E2%29=sqrt%28169-25%29=sqrt%28144%29=12 ALIGN=MIDDLE  ALT=\"CF=sqrt%2813%5E2-5%5E2%29=sqrt%28169-25%29=sqrt%28144%29=12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "BCF and ECD are similar right triangles, because they have a right angle, and congruent angles (actually the same angle) at C.<BR>\n" );
document.write( "The hypotenuse to long leg ratios on triangles BCF and ECD must be the same, because the triangles are similar triangles, so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=EC%2FCD=BC%2FCF ALIGN=MIDDLE  ALT=\"EC%2FCD=BC%2FCF\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=EC%2F6.5=13%2F12 ALIGN=MIDDLE  ALT=\"EC%2F6.5=13%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=EC=6.5%2A13%2F12 ALIGN=MIDDLE  ALT=\"EC=6.5%2A13%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28EC=7%29 ALIGN=MIDDLE  ALT=\"highlight%28EC=7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (rounded)\r<BR>\n" );
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