document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=407869>Question 407869</A>: <I><SPAN STYLE=\"word-break: break-all;\"> TWO PARALLEL CHORDS PQ AND MN ARE 3 cm APART ON THE SAME SIDE OF THE CIRCLE WHERE PQ=7 cm  and  MN = 14cm. CALCULATE THE RADIUS OF THE CIRCLE<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #287401 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=287401\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=MN ALIGN=MIDDLE  ALT=\"MN\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=PQ ALIGN=MIDDLE  ALT=\"PQ\"   DISABLED_style= \"max-width:90%; height:auto;\" > be the parallel chords with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=O ALIGN=MIDDLE  ALT=\"O\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=center ALIGN=MIDDLE  ALT=\"center\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the circle\r<BR>\n" );
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document.write( "given:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+MN=14cm ALIGN=MIDDLE  ALT=\"+MN=14cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=PQ=7cm ALIGN=MIDDLE  ALT=\"PQ=7cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >  with distance <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3cm ALIGN=MIDDLE  ALT=\"3cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > between the parallel chords <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=MN ALIGN=MIDDLE  ALT=\"MN\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=PQ ALIGN=MIDDLE  ALT=\"PQ\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X ALIGN=MIDDLE  ALT=\"X\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y ALIGN=MIDDLE  ALT=\"Y\"   DISABLED_style= \"max-width:90%; height:auto;\" > be the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mid ALIGN=MIDDLE  ALT=\"mid\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+points ALIGN=MIDDLE  ALT=\"+points\"   DISABLED_style= \"max-width:90%; height:auto;\" > of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=MN ALIGN=MIDDLE  ALT=\"MN\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=PQ ALIGN=MIDDLE  ALT=\"PQ\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "Then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=OXY ALIGN=MIDDLE  ALT=\"OXY\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=unique ALIGN=MIDDLE  ALT=\"unique\"   DISABLED_style= \"max-width:90%; height:auto;\" > line which is the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=perpendicular ALIGN=MIDDLE  ALT=\"perpendicular\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+bisector ALIGN=MIDDLE  ALT=\"+bisector\"   DISABLED_style= \"max-width:90%; height:auto;\" >  to both <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=MN ALIGN=MIDDLE  ALT=\"MN\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=PQ ALIGN=MIDDLE  ALT=\"PQ\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "This is the theorem of the line joining the center of the circle and  the mid point of the chord is perpendicular to the chord . \r<BR>\n" );
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document.write( "Or else, a line joining the center of the circle cuts chord perpendicularly, then it bisects the chord.  \r<BR>\n" );
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document.write( "So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=XN+=7cm ALIGN=MIDDLE  ALT=\"XN+=7cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=YQ+=+3.5cm ALIGN=MIDDLE  ALT=\"YQ+=+3.5cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=XY+=+3cm ALIGN=MIDDLE  ALT=\"XY+=+3cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > ..........given\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=XN+=7cm ALIGN=MIDDLE  ALT=\"XN+=7cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=YQ+=+3.5 ALIGN=MIDDLE  ALT=\"YQ+=+3.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >  \r<BR>\n" );
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document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=OX+=+x ALIGN=MIDDLE  ALT=\"OX+=+x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, \r<BR>\n" );
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document.write( "now from the right angled triangle, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=OXN ALIGN=MIDDLE  ALT=\"OXN\"   DISABLED_style= \"max-width:90%; height:auto;\" > , by Pythagoras theorem,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=OX%5E2%2BXN%5E2+=+ON%5E2+=+r%5E2 ALIGN=MIDDLE  ALT=\"OX%5E2%2BXN%5E2+=+ON%5E2+=+r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=radius ALIGN=MIDDLE  ALT=\"radius\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the circle, \r<BR>\n" );
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document.write( "or\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+7%5E2+=+r%5E2 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+7%5E2+=+r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.........................(1)\r<BR>\n" );
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document.write( "Similarly from right triangle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=OYQ ALIGN=MIDDLE  ALT=\"OYQ\"   DISABLED_style= \"max-width:90%; height:auto;\" >,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=OY%5E2%2BYQ%5E2=r%5E2 ALIGN=MIDDLE  ALT=\"OY%5E2%2BYQ%5E2=r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2Bx%29%5E2%2B3.5%5E2+=+r%5E2 ALIGN=MIDDLE  ALT=\"%283%2Bx%29%5E2%2B3.5%5E2+=+r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >...................(2).\r<BR>\n" );
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document.write( "From (1) and (2), left sides must be equal because right sides are equal:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B7%5E2=%28x%2B3%29%5E2%2B%283.5%29%5E2 ALIGN=MIDDLE  ALT=\"x%5E2%2B7%5E2=%28x%2B3%29%5E2%2B%283.5%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B49=x%5E2%2B6x%2B9%2B12.25 ALIGN=MIDDLE  ALT=\"x%5E2%2B49=x%5E2%2B6x%2B9%2B12.25\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=49-21.22+=+6x ALIGN=MIDDLE  ALT=\"49-21.22+=+6x\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x+=+27.75 ALIGN=MIDDLE  ALT=\"6x+=+27.75\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=27.5%2F6+=+4.625+cm ALIGN=MIDDLE  ALT=\"x=27.5%2F6+=+4.625+cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "Therefore, from(1).\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284.625%29%5E2%2B7%5E2+=+r%5E2 ALIGN=MIDDLE  ALT=\"%284.625%29%5E2%2B7%5E2+=+r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+sqrt%28%284.625%29%5E2%2B7%5E2%29+=+8.380012097cm ALIGN=MIDDLE  ALT=\"r+=+sqrt%28%284.625%29%5E2%2B7%5E2%29+=+8.380012097cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+8.38cm ALIGN=MIDDLE  ALT=\"r+=+8.38cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the radius of the circle.\r<BR>\n" );
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