document.write( "Question 1112498: FIND THE COORDINATES OF THE POINT EQUIDISTANT FROM (1, -6), (5, -6) AND (6, 1)
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Algebra.Com's Answer #727555 by ikleyn(52777) $\"\"$ $\"About$

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\n" ); document.write( "The point under the question is the center of the circle subscribed around the triangle with the vertices at the given points.\r
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\n" ); document.write( "\n" ); document.write( "The center of this triangle is the intersection point of any two perpendicular bisectors to the triangle sides.\r
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\n" ); document.write( "\n" ); document.write( "So, I will search for intersection point of the two perpendicular bisectors.\r
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document.write( "Let  A = (1,-6),  B = (5,-6) and  C = (6,1).\r\n" );
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document.write( "One side of the triangle, AB, is horizontal  y= -6.\r\n" );
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document.write( "Its midpoint is  D = (3,-6).\r\n" );
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document.write( "The perpendicular bisector to this segment is the line  x= 3.\r\n" );
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document.write( "The side AC  has the slope   = .\r\n" );
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document.write( "The midpoint of this side is  E = (3.5,-2.5)\r\n" );
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document.write( "The perpendicular bisector to AC through the mid-point E  has the equation \r\n" );
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document.write( "y+2.5 = \r\n" );
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document.write( "The intersection point of the two perpendicular bisectors is  y+2.5 =  =  =  =   ====>  \r\n" );
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document.write( "y =  - 2.5 =  -  =  =  = .\r\n" );
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document.write( "Answer.  The point under the question is (3,).\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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