document.write( "Question 1186877: Find the equation of the circle touching the lines 3x + 4y = 12, 4x +3y = 9 and having its center on the line 3x + y = 7 \n" ); document.write( "

Algebra.Com's Answer #817870 by Alan3354(69443) $\"\"$ $\"About$

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Find the equation of the circle touching (tangent to) the lines
\n" ); document.write( "L1, 3x + 4y = 12,
\n" ); document.write( "L2, 4x +3y = 9 and having its center on the line
\n" ); document.write( "L3, 3x + y = 7
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\n" ); document.write( "Find the intersection of L3 with L1 and L2. The center C is the midpoint of those 2 points.
\n" ); document.write( "The distance from C to L1 or L2 is the radius.
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\n" ); document.write( "Only one circle is possible.
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\n" ); document.write( "If L3 was the bisector of L1 and L2, an infinite # of circles would fit, but it is not.
\n" ); document.write( "If the 3 lines intersected at the same point, but L3 was not the bisector, no solution is possible.
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\n" ); document.write( "PS The problem is more interesting than a lot of the ones posted. It became clear to me after I graphed the 3 lines.
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