document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=772294>Question 772294</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1.Find the equation of the ciecle inscribed in a triangle, if the triangle has its sides on the line; 2x + y - 9 = 0, -2x + y - 1 = 0, and -x + 2y + 7 = 0. Draw the figure.\r<BR>\n" );
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document.write( "2.identify the points of the ellipse 4x^2 + 5y^2 - 8x + 20y = -24.\r<BR>\n" );
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document.write( "3. Find the vertices, foci, eccentricity, and lenght of the latus rectum of the ellipse x^2 + 16y^2 = 16. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #470774 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=470774\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "The perpendicular bisectors of the three sides of any triangle intersect in a point called the <i>circumcenter</i> which is a point equidistant from each of the sides and is therefore the center of the inscribed circle; said circle having a radius equal to the distance from the circumcenter to any one of the sides.\r<BR>\n" );
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document.write( "Step 1:  Find one vertex of the triangle by solving the 2X2 linear system comprised of two of the equations of lines containing segments representing the sides of the triangle.\r<BR>\n" );
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document.write( "Step 2:  Repeat step 1 twice more so that you have solved for the intersection of each of the three pairs of sides thereby identifying all three vertices.\r<BR>\n" );
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document.write( "Step 3:  Using the mid-point formulas and the coordinates of the three vertices, determine the mid points of two of the sides.\r<BR>\n" );
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document.write( "Step 4:  Using the equation for the line containing one of the segments for which you determined a mid-point in step 3, calculate the slope of the line containing that side.\r<BR>\n" );
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document.write( "Step 5:  Repeat step 4 for the other side for which you have calculated a mid-point.\r<BR>\n" );
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document.write( "Step 6:  Using the point-slope form of an equation of a line, the slope you calculated in step 4, and the corresponding mid-point, derive the equation of the perpendicular bisector of that side.\r<BR>\n" );
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document.write( "Step 7:  Repeat step 6 for the other side for which you have a slope and a midpoint.\r<BR>\n" );
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document.write( "Step 8:  Solve the 2X2 system formed by the equations derived in steps 6 and 7.\r<BR>\n" );
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document.write( "Step 9:  The solution from step 8 is the ordered pair representing the center of the inscribed circle.  Using that center point and either of the midpoints calculated in step 3 in the distance formula, calculate the radius of the inscribed circle.  For convenience, leave the result in <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE r^2\"> form.\r<BR>\n" );
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document.write( "Step 10:  Using the coordinates of the center from step 8 and the value of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE r^2\"> from step 9, write the equation of the inscribed circle:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ (x\ -\ h)^2\ +\ (y\ -\ k)^2\ =\ r^2\">\r<BR>\n" );
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document.write( "Where <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE (h,\,k)\"> is the center of the circle and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE r\"> is the radius.\r<BR>\n" );
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document.write( "This problem requires that you take it slowly, checking your work after each step.  One little sign error in an early step will turn into hours of drugery.\r<BR>\n" );
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document.write( "By the way, if you are wondering what happened to the other two problems you posted, go back and re-read the instruction that says \"One question per post\".  Then you can stop wondering, right?<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "<font face=\"Math1\" size=\"+2\">Egw to Beta kai to Sigma</font><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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