document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206348>Question 1206348</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two chords and a diameter form a triangle inside a circle. The radius is 5cm and one chord is 2cm longer than the other. Find the perimeter and area of the triangle </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #843740 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=843740\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Apply Thales Theorem to determine we have a right triangle.<BR>\n" );
document.write( "Thales Theorem is a special case of the Inscribed Angle Theorem.<BR>\n" );
document.write( "This is what your diagram would look like (imagine adding the proper labels)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" width=300 src=\"https://upload.wikimedia.org/wikipedia/commons/thumb/4/44/Thales%27_Theorem_Simple.svg/1024px-Thales%27_Theorem_Simple.svg.png\"><BR>\n" );
document.write( "Image credit:<BR>\n" );
document.write( "<a  rel=nofollow HREF=\"https://en.wikipedia.org/wiki/Thales%27s_theorem\">https://en.wikipedia.org/wiki/Thales%27s_theorem</a>\r<BR>\n" );
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document.write( "radius = 5<BR>\n" );
document.write( "diameter = 2*radius = 2*5 = 10<BR>\n" );
document.write( "The diameter is the hypotenuse of the right triangle. <BR>\n" );
document.write( "A diameter is a special type of chord that passes through the center. It's the longest chord of the circle.\r<BR>\n" );
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document.write( "x = shorter leg of the right triangle<BR>\n" );
document.write( "x+2 = longer leg of the right triangle<BR>\n" );
document.write( "x > 0 since a negative side length makes no sense.\r<BR>\n" );
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document.write( "Due to the Pythagorean Theorem <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Bb%5E2=c%5E2 ALIGN=MIDDLE  ALT=\"a%5E2%2Bb%5E2=c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can say <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B%28x%2B2%29%5E2+=+10%5E2 ALIGN=MIDDLE  ALT=\"x%5E2%2B%28x%2B2%29%5E2+=+10%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let's expand things out to solve for x.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B%28x%2B2%29%5E2+=+10%5E2 ALIGN=MIDDLE  ALT=\"x%5E2%2B%28x%2B2%29%5E2+=+10%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B%28x%2B2%29%28x%2B2%29+=+100 ALIGN=MIDDLE  ALT=\"x%5E2%2B%28x%2B2%29%28x%2B2%29+=+100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Bx%5E2%2B4x%2B4+=+100 ALIGN=MIDDLE  ALT=\"x%5E2%2Bx%5E2%2B4x%2B4+=+100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B4x%2B4+=+100 ALIGN=MIDDLE  ALT=\"2x%5E2%2B4x%2B4+=+100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B4x%2B4-100=0 ALIGN=MIDDLE  ALT=\"2x%5E2%2B4x%2B4-100=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B4x-96=0 ALIGN=MIDDLE  ALT=\"2x%5E2%2B4x-96=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x%5E2%2B2x-48%29=0 ALIGN=MIDDLE  ALT=\"2%28x%5E2%2B2x-48%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x%2B8%29%28x-6%29+=+0 ALIGN=MIDDLE  ALT=\"2%28x%2B8%29%28x-6%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B8=0 ALIGN=MIDDLE  ALT=\"x%2B8=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-6+=+0 ALIGN=MIDDLE  ALT=\"x-6+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-8 ALIGN=MIDDLE  ALT=\"x+=+-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+6 ALIGN=MIDDLE  ALT=\"x+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The quadratic formula is an alternative approach.<BR>\n" );
document.write( "Ignore the negative result because we stated x > 0 earlier.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+6 ALIGN=MIDDLE  ALT=\"x+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" > leads to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2+=+6%2B2+=+8 ALIGN=MIDDLE  ALT=\"x%2B2+=+6%2B2+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We have a 6-8-10 right triangle.\r<BR>\n" );
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document.write( "perimeter = add the sides = 6+8+10 = <font color=red>24 cm</font><BR>\n" );
document.write( "area = 0.5*base*height = 0.5*6*8 = <font color=red>24 square cm</font><BR>\n" );
document.write( "This is one of the fairly rare moments when the perimeter and area are the same value (except for the differing unit types of course).<BR>\n" );
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