document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=746229>Question 746229</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please help me solve this equation ; the circle is divided into 4 parts a,b,c,d where part a & c form a semicircle and part b&d form the other semicircle area of part a to area of part c is in the ratio 1: 3 the area of part b to the area of part d is in the ratio 1:2. the area of part c is bigger than part b by 20 SquareCentimeters find the area of the whole cirle </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #454196 by </B><A HREF=/tutors/aboutme.mpl?userid=savvyhush23><B>savvyhush23(50)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=savvyhush23><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=savvyhush23><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=454196\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> please help me solve this equation ; the circle is divided into 4 parts a,b,c,d where part a & c form a semicircle and part b&d form the other semicircle area of part a to area of part c is in the ratio 1: 3 the area of part b to the area of part d is in the ratio 1:2. the area of part c is bigger than part b by 20 SquareCentimeters find the area of the whole cirle.<BR>\n" );
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document.write( "Ok, let solve it one by one,<BR>\n" );
document.write( "Let,<BR>\n" );
document.write( "At = Total area of circle<BR>\n" );
document.write( "Aa = Area of a<BR>\n" );
document.write( "Ab = Area of b<BR>\n" );
document.write( "Ac = Area of c<BR>\n" );
document.write( "Ad = Area of d<BR>\n" );
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document.write( "part a & c form a semicircle...part b&d form the other semicircle:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=At%2F2+=+Aa+%2B+Ac ALIGN=MIDDLE  ALT=\"At%2F2+=+Aa+%2B+Ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=At%2F2+=+Ab+%2B+Ad ALIGN=MIDDLE  ALT=\"At%2F2+=+Ab+%2B+Ad\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "part a to area of part c is in the ratio 1:3...<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Aa%2FAc=1%2F3 ALIGN=MIDDLE  ALT=\"Aa%2FAc=1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Ac=3Aa ALIGN=MIDDLE  ALT=\"Ac=3Aa\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "part b to the area of part d is in the ratio 1:2...<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Ab%2FAd=1%2F2 ALIGN=MIDDLE  ALT=\"Ab%2FAd=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Ad=2Ab ALIGN=MIDDLE  ALT=\"Ad=2Ab\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "the area of part c is bigger than part b by 20...<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Ac+=+Ab+%2B+20 ALIGN=MIDDLE  ALT=\"Ac+=+Ab+%2B+20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Ok, here is my favorite part:<BR>\n" );
document.write( "We have 5 unknown (At, Aa, Ab, Ac, and Ad), so we have to form 5 equations to solve it. The 4 equations are ready above, <BR>\n" );
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document.write( "since a & c and b & d are semi circle, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=At%2F2=At%2F2 ALIGN=MIDDLE  ALT=\"At%2F2=At%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, equation 5<BR>\n" );
document.write( "we have the 2 equations for that above, substituting here, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Aa+%2B+Ac+=+Ab+%2B+Ad ALIGN=MIDDLE  ALT=\"Aa+%2B+Ac+=+Ab+%2B+Ad\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-Aa+%2B+Ab+-+Ac+%2B+Ad+=+0 ALIGN=MIDDLE  ALT=\"-Aa+%2B+Ab+-+Ac+%2B+Ad+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then add this to the other 3 remaining equation: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-Aa+%2B+Ab+-+Ac+%2B+Ad%29+%2B+%283Aa-Ac%29+%2B+%282Ab-Ad%29+%2B+%28-Ab+%2B+Ac+-+20%29+=+2Aa+%2B+2Ab+-+Ac+-+20=0 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "but <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+Aa+=+Ac%2F3 ALIGN=MIDDLE  ALT=\"+Aa+=+Ac%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Ab=Ac-20 ALIGN=MIDDLE  ALT=\"Ab=Ac-20\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28Ac%2F3%29+%2B+2%28Ac-20%29-+Ac+-+20=0 ALIGN=MIDDLE  ALT=\"2%28Ac%2F3%29+%2B+2%28Ac-20%29-+Ac+-+20=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Ac+=+36+cm%5E2 ALIGN=MIDDLE  ALT=\"Ac+=+36+cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Ab+=+16+cm%5E2 ALIGN=MIDDLE  ALT=\"Ab+=+16+cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Ad=32+cm%5E2 ALIGN=MIDDLE  ALT=\"Ad=32+cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Aa=12+cm%5E2 ALIGN=MIDDLE  ALT=\"Aa=12+cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Therefore, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=At+=+Aa+%2B+Ab+%2B+Ac+%2B+Ad+=+96+cm%5E2 ALIGN=MIDDLE  ALT=\"At+=+Aa+%2B+Ab+%2B+Ac+%2B+Ad+=+96+cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Check it, the value of individual area must satisfy the given ratio. </SPAN>\n" );
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