document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=121820>Question 121820</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello, \r<BR>\n" );
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document.write( "I have a question that I am having a lot of trouble with. I'll give you the question and try to explain (as best as I can) my working out so far and hopefully you'll be able to understand it and give me a detailed explanation of the answer. :^) \r<BR>\n" );
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document.write( "I think you might need a diagram to visualise the whole thing which I cannot actually draw, however, I'll do my best to describe it. (If you would like a similar picture I checked Google Images and did find an image that closely resembled what the question was. Except for the circle at the base of the larger circle, everything is correct. Insert the measurements and that's <BR>\n" );
document.write( "how it looks like. The link is: http://mimosa.cnice.mecd.es/~jcolon/tangen.gif\r<BR>\n" );
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document.write( "THE QUESTION<BR>\n" );
document.write( "Here it is: \r<BR>\n" );
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document.write( "Imagine a circle and a isosceles triangle is in it, each of its vertices touching the edges of the circle. The top vertice is labelled P and the two bottom vertices from left to right is labelled Q and R. (I hope you can either visualise it or sketch it on a piece of paper) QR = 18 and PQ = PR = 15. The questions asks me/you: What is the radius of the circle? \r<BR>\n" );
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document.write( "MY WORKING OUT<BR>\n" );
document.write( "I drew a line bisecting the triangle PQR in the way you told me to and extended it down to the diameter of the circle. Then I labelled the diameter PS and the intersection of PS and QR: T. I now have two right-angled triangles where I can label each side length a, b and c (the hypotenuse). \r<BR>\n" );
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document.write( "a = the side length I need to find<BR>\n" );
document.write( "b = T-R or T-Q (halve 18 [Q-R) = 9<BR>\n" );
document.write( "c = hypotenuse (15)\r<BR>\n" );
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document.write( "I then applied the Pythagorean Theorem to find (a) which is the side length I need to find, n amelly the segment PT. Using the Pythagorean Theorem PT = 12. All I needed to find now was the segment TS and in order to do that I needed to find the segment QS, and if I connect them I form another two triangles (QTS) and (PSQ) and I can use the sides of PTQ to work it out. But I'm stuck. I <BR>\n" );
document.write( "don't know where to go from here.\r<BR>\n" );
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document.write( "Please help, because Im not sure what to do next. Do I have to understand trigonometry, or geometry or more about triangles to solve it? I was told by my teacher there is a special relationship between the triangles PQS, PTQ and QTS. But I don't know what. \r<BR>\n" );
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document.write( "Thanks, \r<BR>\n" );
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document.write( "Jasmine (13)  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #89573 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=89573\">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%28+400%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%0D%0A++line%28+-9%2C+-9%2C+-9%2C+9+%29%2C%0D%0A++line%28+-9%2C++9%2C++0%2C+-9+%29%2C%0D%0A++line%28+-9%2C+-9%2C++0%2C+-9+%29%2C%0D%0A++line%28+-9%2C+-3%2C++0%2C+-9%29%2C%0D%0A++line%28+-9%2C+-8.5%2C++-8.5%2C+-8.5%29%2C%0D%0A++line%28+-8.5%2C+-9%2C+-8.5%2C+-8.5%29%2C%0D%0A++locate%28+-9.5%2C+-2.5%2C+C+%29%2C%0D%0A++locate%28+-9.5%2C+9.5%2C+P+%29%2C%0D%0A++locate%28+-9.5%2C+-9%2C+T+%29%2C%0D%0A++locate%28++0.5%2C+-9%2C+R+%29%2C%0D%0A++locate%28+-4%2C+-9.5%2C+9+%29%2C%0D%0A++locate%28+-4%2C+1.5%2C+15+%29%0D%0A++%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK, I think I've made a representation using the letters that you provided. <BR>\n" );
document.write( "All you need is the Pythagorean theorem. <BR>\n" );
document.write( "Point P and R are on the circle. I don’t show point Q. <BR>\n" );
document.write( "The distance of PR is 15. <BR>\n" );
document.write( "The length of TR is 1/2(18) or 9.<BR>\n" );
document.write( "C is the center of the circle. <BR>\n" );
document.write( "PC and CR are radii of the circle. <BR>\n" );
document.write( "There are two right triangles that you use to solve for the radius of the circle. <BR>\n" );
document.write( "Let’s call the radius G since R is already taken.<BR>\n" );
document.write( "The first triangle is CRT with sides CT, TR (9), and hypotenuse CR(G). <BR>\n" );
document.write( "Let CT = a. Then,<BR>\n" );
document.write( "1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+%2B+9%5E2+=+G+%5E2 ALIGN=MIDDLE  ALT=\"a%5E2+%2B+9%5E2+=+G+%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "The second triangle is PRT with sides PT(G+a), TR(9), and hypotenuse PR(15). <BR>\n" );
document.write( "2.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28G%2Ba%29%5E2%2B9%5E2=15%5E2 ALIGN=MIDDLE  ALT=\"%28G%2Ba%29%5E2%2B9%5E2=15%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "From 2,<BR>\n" );
document.write( "2.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28G%2Ba%29%5E2%2B9%5E2=15%5E2 ALIGN=MIDDLE  ALT=\"%28G%2Ba%29%5E2%2B9%5E2=15%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28G%2Ba%29%5E2=15%5E2-9%5E2 ALIGN=MIDDLE  ALT=\"%28G%2Ba%29%5E2=15%5E2-9%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28G%2Ba%29%5E2=144 ALIGN=MIDDLE  ALT=\"%28G%2Ba%29%5E2=144\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=G%2Ba=12 ALIGN=MIDDLE  ALT=\"G%2Ba=12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=G=12-a ALIGN=MIDDLE  ALT=\"G=12-a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substitute that result into 1.<BR>\n" );
document.write( "1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+%2B+9%5E2+=+G+%5E2 ALIGN=MIDDLE  ALT=\"a%5E2+%2B+9%5E2+=+G+%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+%2B+81+=+%2812-a%29%5E2 ALIGN=MIDDLE  ALT=\"a%5E2+%2B+81+=+%2812-a%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+%2B+81+=+144-24a%2Ba%5E2 ALIGN=MIDDLE  ALT=\"a%5E2+%2B+81+=+144-24a%2Ba%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24a=63 ALIGN=MIDDLE  ALT=\"24a=63\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=63%2F24 ALIGN=MIDDLE  ALT=\"a=63%2F24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=21%2F8 ALIGN=MIDDLE  ALT=\"a=21%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "From 2,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=G=12-a ALIGN=MIDDLE  ALT=\"G=12-a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=G=96%2F8-21%2F8 ALIGN=MIDDLE  ALT=\"G=96%2F8-21%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=G=75%2F8 ALIGN=MIDDLE  ALT=\"G=75%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The radius of the circle is 75/8.  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );