document.write( "Question 830212: Could you please solve this for me. Your assistance is always honored.\r
\n" ); document.write( "\n" ); document.write( "* Find the equation of a circle inscribed in atriangle, if the
\n" ); document.write( "triangle has its sides on the lines;
\n" ); document.write( "2x + y - 9 = 0, -2x + y - 1= 0, and -x + 2y + 7 = 0. Draw the figure. \n" ); document.write( "

Algebra.Com's Answer #541501 by AnlytcPhil(1806) $\"\"$ $\"About$

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document.write( "2x + y - 9 = 0,   -2x + y - 1= 0, and -x + 2y + 7 = 0.\r\n" );
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document.write( "Let its equation be \r\n" );
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document.write( "The inscribed circle must be such that the perpendicular \r\n" );
document.write( "distance from its center (h,k) to each of the three lines \r\n" );
document.write( "must all be equal and be equal to the radius r of the \r\n" );
document.write( "inscribed circle. \r\n" );
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document.write( "d = \r\n" );
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document.write( "Use distance from point to line formula:\r\n" );
document.write( "d = \r\n" );
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document.write( "For the first line\r\n" );
document.write( "r = \r\n" );
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document.write( "r = \r\n" );
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document.write( "r = \r\n" );
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document.write( "For the second line\r\n" );
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document.write( "r = \r\n" );
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document.write( "r = \r\n" );
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document.write( "r = \r\n" );
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document.write( "For the third line\r\n" );
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document.write( "r = \r\n" );
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document.write( "r = \r\n" );
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document.write( "r = \r\n" );
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document.write( "Absolute value equations often have more than one solution, but we are\r\n" );
document.write( "only interested in a solution that is inside the triangle.  So we can discard\r\n" );
document.write( "any solution that cannot be inside the triangle.  So we graph the three lines\r\n" );
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document.write( "Setting the first two equal\r\n" );
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document.write( " or \r\n" );
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document.write( " or \r\n" );
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document.write( " or \r\n" );
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document.write( " or \r\n" );
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document.write( "We can disregard k=5 because no point with y-coordinate 5 could be the\r\n" );
document.write( "y-coordinate of the inscribed circle. However h=2 is a candidate for\r\n" );
document.write( "the x-coordinate of the radius of the inscribed circle.\r\n" );
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document.write( "Setting the first and third equal\r\n" );
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document.write( " or \r\n" );
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document.write( " or \r\n" );
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document.write( " or \r\n" );
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document.write( " or \r\n" );
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document.write( "That's the same. 2 is so far the only candidate for h.  Let's set the second and\r\n" );
document.write( "third equal:\r\n" );
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document.write( " or  \r\n" );
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document.write( " or \r\n" );
document.write( " or \r\n" );
document.write( " or \r\n" );
document.write( " or \r\n" );
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document.write( "If h=2 then if we substitute in those, we get:\r\n" );
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document.write( " or \r\n" );
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document.write( " or \r\n" );
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document.write( " or \r\n" );
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document.write( "We can disregard -10 so the center of the inscribed circle must be\r\n" );
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document.write( "(h,k) = (2.0)\r\n" );
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document.write( "So we find the radius by substituting in any one of the three equations\r\n" );
document.write( "for the radius, say, the first one\r\n" );
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document.write( "r = \r\n" );
document.write( "r = \r\n" );
document.write( "r = \r\n" );
document.write( "r = \r\n" );
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document.write( "r = \r\n" );
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document.write( "rationalize the denominator\r\n" );
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document.write( "r = \r\n" );
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document.write( "That makes\r\n" );
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document.write( "So the equation is\r\n" );
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document.write( "{{x-2)^2+(y-0)^2=5}}}\r\n" );
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document.write( "{{x-2)^2+y^2=5}}}\r\n" );
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document.write( "Edwin

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