Lines y=x+2, 4y=3x+6 and 3y=4x+1 are tangents to the circle (x−h)2+(y−k)2=r2.
Centre of the circle is (h,k).
Equation of bisector of lines 4y=3x+6,3y=4x+1 is:
54x−3y+1=±(53x−4y+6)
⇒4x−3y+1=±(3x−4y+6)
Taking positive sign, we get
4x−3y+1=3x−4y+6
⇒x+y=5
Since, centre (h,k) lies on the bisector, therefore
h+k=5