document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=85770>Question 85770</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A diameter that is perpendicular to a chord___the chord and its arc\r<BR>\n" );
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document.write( "Tangents to a circle from a point are (a)___ and (b) each tangent is ___ to the radius drawn to the point of tangency </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #61972 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20056)</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=61972\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A diameter that is perpendicular to a chord___the chord and its arc\r<BR>\n" );
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document.write( "Let's draw a circle:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C400%2C-2%2C+2%2C+-2%2C2%2C+circle%280%2C0%2C1%29%29 ALIGN=MIDDLE  ALT=\"drawing%28400%2C400%2C-2%2C+2%2C+-2%2C2%2C+circle%280%2C0%2C1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Now let's draw a chord:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C400%2C-2%2C+2%2C+-2%2C2%2C+circle%280%2C0%2C1%29%2Cline%28cos%281%29%2Csin%281%29%2Ccos%28-.4%29%2Csin%28-.4%29%29%0D%0A+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >   \r<BR>\n" );
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document.write( "Now let's draw a diameter perpendicular to that chord\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C400%2C-2%2C+2%2C+-2%2C2%2C+circle%280%2C0%2C1%29%2Cline%28cos%281%29%2Csin%281%29%2Ccos%28-.4%29%2Csin%28-.4%29%29%2C+line%28cos%28.3%29%2Csin%28.3%29%2C-cos%28.3%29%2C-sin%28.3%29%29++%0D%0A+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "As you can see from the figure, that diameter bisects both the chord and its<BR>\n" );
document.write( "arc.  The word is \"bisects\". \r<BR>\n" );
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document.write( "-------------------------------------------------------------------\r<BR>\n" );
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document.write( "Tangents to a circle from a point are (a)___ and (b) each tangent is ___ to the radius drawn to the point of tangency\r<BR>\n" );
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document.write( "Draw a circle:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C200%2C-9%2C+18%2C+-9%2C9%2C+circle%280%2C0%2C8%29+%0D%0A+%29 ALIGN=MIDDLE  ALT=\"drawing%28300%2C200%2C-9%2C+18%2C+-9%2C9%2C+circle%280%2C0%2C8%29+%0D%0A+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Draw two tangents from an arbitrary point outside the circle:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C200%2C-9%2C+18%2C+-9%2C9%2C+circle%280%2C0%2C8%29%2C+line%2864%2F17%2C120%2F17%2C17%2C0%29%2Cline%2864%2F17%2C-120%2F17%2C17%2C0%29+++%0D%0A+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "They sure do look equal in lengthe, so the word you want for (a) is \"equal\"\r<BR>\n" );
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document.write( "Draw in an upper radius to the upper point of tangency:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C200%2C-9%2C+18%2C+-9%2C9%2C+circle%280%2C0%2C8%29%2Cline%280%2C0%2C64%2F17%2C120%2F17%29%2Cline%2864%2F17%2C120%2F17%2C17%2C0%29%2C+line%2817%2C0%2C64%2F17%2C-120%2F17%29+++%0D%0A+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "It certainly looks like that upper radius is perpendicular to the upper tangent.\r<BR>\n" );
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document.write( "Draw in a lower radius to the lower point of tangency:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C200%2C-9%2C+18%2C+-9%2C9%2C+circle%280%2C0%2C8%29%2Cline%280%2C0%2C64%2F17%2C120%2F17%29%2C+line%2864%2F17%2C120%2F17%2C17%2C0%29%2C+line%2864%2F17%2C-120%2F17%2C17%2C0%29%2C+line%280%2C0%2C64%2F17%2C-120%2F17%29+++%0D%0A+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "It certainly looks like that lower radius is perpendicular to the lower <BR>\n" );
document.write( "tangent.\r<BR>\n" );
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document.write( "So the word for (b) is \"perpendicular\".\r<BR>\n" );
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document.write( "Edwin </SPAN>\n" );
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