According to the question, circles are drawn as shown in the figure.
Centre of the circles lies on one of the angle bisectors of the given lines.
`(5x+12y-10)/(13)= +- (5x-12y-40)/(13)`
or `24y=-30` and `10x=50`
But centre lies in first quadrant.
So, for centre , `x=5`.
Distance of centre (C(5,y) from the line `5x+12y-10=0` is 3.
`:. (5(5)+12y-10)/(13)= +-13`
`:. y=2` (As centre lies in first quadrant)
Sol, centre is (5,2).
Alsok, in right angles triangle CMR, `CR=5(` as `RM=4)`.
Hence, equation of circle is `(x-5)^(2)-(y-2)^(2)=5^(2)`.
