document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=859829>Question 859829</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Each side of the right triangle ABC is tangent to the circle with center o. The radius of the circle is 4 inches and the length AC is 12 inches. Find each of the following. \r<BR>\n" );
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document.write( "m&#8736;C (Angle C)<BR>\n" );
document.write( "m&#8736;B (Angle B)<BR>\n" );
document.write( "Line BC\r<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 #518142 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20060)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><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=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=518142\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Each side of the right triangle ABC is tangent to the circle with center O. The radius of the circle is 4 inches and the length AC is 12 inches. Find each of the following. <BR>\n" );
document.write( "m&#8736;C (Angle C)<BR>\n" );
document.write( "m&#8736;B (Angle B)<BR>\n" );
document.write( "Line BC<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C320%2C-2%2C18%2C-2%2C14%2C%0D%0A+locate%28-.8%2C6%2C12%29%2C+green%28line%280%2C4%2C4%2C4%29%2Clocate%282%2C4%2C4%29%29%2C%0D%0Alocate%280%2C0%2CA%29%2Clocate%2816%2C0%2CB%29%2C+locate%280%2C13%2CC%29%2C%0D%0A+%0D%0Acircle%284%2C4%2C0.15%29%2Ccircle%284%2C4%2C0.13%29%2Ccircle%284%2C4%2C0.11%29%2Ccircle%284%2C4%2C0.09%29%2Ccircle%284%2C4%2C0.07%29%2Ccircle%284%2C4%2C0.05%29%2Ccircle%284%2C4%2C0.03%29%2Ccircle%284%2C4%2C0.01%29%2C%0D%0Alocate%284.2%2C3.8%2CO%29%2C%0D%0A+%0D%0A%0D%0Atriangle%280%2C0%2C0%2C12%2C16%2C0%29%2C+circle%284%2C4%2C4%29+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Draw radii (in green) to the three points of tangency,<BR>\n" );
document.write( "OD, OE, and OF, which are perpendicular to the three<BR>\n" );
document.write( "sides.  Draw OC and OB.  Extend FO till it intersects BC at G.<BR>\n" );
document.write( "Then draw GH&#8869;AB<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C320%2C-2%2C18%2C-2%2C14%2C%0D%0A+%0D%0Alocate%280%2C0%2CA%29%2Clocate%2816%2C0%2CB%29%2C+locate%280%2C13%2CC%29%2C%0D%0Ared%28line%284%2C4%2C0%2C12%29%2Cline%284%2C4%2C16%2C0%29%29%2C%0D%0Acircle%284%2C4%2C0.15%29%2Ccircle%284%2C4%2C0.13%29%2Ccircle%284%2C4%2C0.11%29%2Ccircle%284%2C4%2C0.09%29%2Ccircle%284%2C4%2C0.07%29%2Ccircle%284%2C4%2C0.05%29%2Ccircle%284%2C4%2C0.03%29%2Ccircle%284%2C4%2C0.01%29%2C%0D%0Alocate%284.2%2C3.8%2CO%29%2Clocate%282%2C4%2C4%29%2Clocate%284.7%2C6.5%2C4%29%2C%0D%0Agreen%28line%284%2C0%2C4%2C4%29%2Cline%280%2C4%2C4%2C4%29%2Cline%284%2C4%2C6.4%2C7.2%29%2Cline%284%2C4%2C32%2F3%2C4%29%2C%0D%0A+%0D%0Aline%2832%2F3%2C0%2C32%2F3%2C4%29%29%2Clocate%2832%2F3%2C0%2CH%29%2Clocate%284%2C9.8%2C8%29%2C%0D%0Alocate%288%2C7.7%2C16%2F3%29%2C+locate%2813%2C4%2C20%2F3%29%2C%0D%0A+%0D%0Alocate%284%2C0%2CD%29%2Clocate%286.6%2C8%2CE%29%2C+locate%28-.6%2C4.3%2CF%29%2C%0D%0Alocate%28-.5%2C2.2%2C4%29%2Clocate%28-.5%2C8%2C8%29%2Clocate%28-.5%2B4%2C2.2%2C4%29%2C%0D%0Alocate%2810.7%2C4.7%2CG%29%2Clocate%286.5%2C5%2C20%2F3%29%2C%0D%0Atriangle%280%2C0%2C0%2C12%2C16%2C0%29%2C+circle%284%2C4%2C4%29+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "OD=4, so AF=4, and since AC=12, FC=8<BR>\n" );
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document.write( "&#8736;FCO = &#8736;ECG because the center of inscribed circle O<BR>\n" );
document.write( "is the intersection of the angle bisectors.<BR>\n" );
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document.write( "&#916;CFO = &#916;CEO   hypotenuse and a side equal<BR>\n" );
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document.write( "&#8736;FOC &#8773; &#8736;EOC<BR>\n" );
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document.write( "&#8736;FOE = 2&#8736;FOC, CF = CE = 8<BR>\n" );
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document.write( "tan(&#8736;FOC) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=FC%2FOF ALIGN=MIDDLE  ALT=\"FC%2FOF\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2F4 ALIGN=MIDDLE  ALT=\"8%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2<BR>\n" );
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document.write( "CE = CF = 8<BR>\n" );
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document.write( "tan(&#8736;FOE) = tan(&#8736;FOC) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2tan%28FOC%29%2F%281-tan%5E2%28FOC%29%29 ALIGN=MIDDLE  ALT=\"2tan%28FOC%29%2F%281-tan%5E2%28FOC%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%282%29%2F%281-2%5E2%29 ALIGN=MIDDLE  ALT=\"2%282%29%2F%281-2%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F%28-3%29 ALIGN=MIDDLE  ALT=\"4%2F%28-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2F3 ALIGN=MIDDLE  ALT=\"-4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "&#8736;GOE = 180°-&#8736;FOE<BR>\n" );
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document.write( "tan(&#8736;GOE) = 180°-&#8736;FOE<BR>\n" );
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document.write( "tan(&#8736;GOE) = tan(180°-&#8736;FOE) = -tan(&#8736;FOE) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28-4%2F3%29 ALIGN=MIDDLE  ALT=\"-%28-4%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F3 ALIGN=MIDDLE  ALT=\"4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "tan(&#8736;GOE) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=EG%2FOE ALIGN=MIDDLE  ALT=\"EG%2FOE\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=EG%2F4 ALIGN=MIDDLE  ALT=\"EG%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=EG%2F4 ALIGN=MIDDLE  ALT=\"EG%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F3 ALIGN=MIDDLE  ALT=\"4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "EG = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%2F3 ALIGN=MIDDLE  ALT=\"16%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "OG = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28OE%5E2%2BEG%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28OE%5E2%2BEG%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%284%5E2%2B%2816%2F3%29%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%284%5E2%2B%2816%2F3%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2816%2B256%2F9%29 ALIGN=MIDDLE  ALT=\"sqrt%2816%2B256%2F9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28400%2F9%29 ALIGN=MIDDLE  ALT=\"sqrt%28400%2F9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%2F3 ALIGN=MIDDLE  ALT=\"20%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "&#916;OEG &#8773; &#916;GHB   because DE=GH=4 and &#8736;GBH = &#8736;OGE<BR>\n" );
document.write( "                parallel lines FG,AB cut by<BR>\n" );
document.write( "                transversal BC  <BR>\n" );
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document.write( "GB = OG = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%2F3 ALIGN=MIDDLE  ALT=\"20%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "BC = CE + EG + GB = 8 + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%2F3 ALIGN=MIDDLE  ALT=\"16%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%2F3 ALIGN=MIDDLE  ALT=\"20%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60%2F3 ALIGN=MIDDLE  ALT=\"60%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 20\r<BR>\n" );
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document.write( "&#8736;C = &#8736;ACB = cos<sup>-1</sup><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28AC%2FBC%29 ALIGN=MIDDLE  ALT=\"%28AC%2FBC%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = cos<sup>-1</sup><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2812%2F20%29 ALIGN=MIDDLE  ALT=\"%2812%2F20%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = cos<sup>-1</sup><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2F5%29 ALIGN=MIDDLE  ALT=\"%283%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, approximately 53.13°<BR>\n" );
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document.write( "&#8736;B = &#8736;ABC = sin<sup>-1</sup><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28AC%2FBC%29 ALIGN=MIDDLE  ALT=\"%28AC%2FBC%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = sin<sup>-1</sup><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2812%2F20%29 ALIGN=MIDDLE  ALT=\"%2812%2F20%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = sin<sup>-1</sup><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2F5%29 ALIGN=MIDDLE  ALT=\"%283%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, approximately 36.87°\r<BR>\n" );
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document.write( "Edwin</pre> </SPAN>\n" );
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