Question 1186877
Find the equation of the circle touching (tangent to) the lines 
L1, 3x + 4y = 12, 
L2, 4x +3y = 9 and having its center on the line 
L3, 3x + y = 7
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Find the intersection of L3 with L1 and L2.  The center C is the midpoint of those 2 points.
The distance from C to L1 or L2 is the radius.
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Only one circle is possible.
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If L3 was the bisector of L1 and L2, an infinite # of circles would fit, but it is not.
If the 3 lines intersected at the same point, but L3 was not the bisector, no solution is possible.
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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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