Finding the equation of the circle which touches the pair of lines $7x^2 - 18xy +7 y^2 = 0$ and the circle $x^2 + y^2 - 8x -8y = 0$ and contained in the given circle??
My attempt The centre of required circle would lie on angle bisector of the pair of lines ie $x=y$.
Assuming circle to be $(x-h)^2+(y-h)^2=r^2$
Now $2(h-8)^2=r^2$ ( distance between the extreme of larger circle and center of contained circle,)
I am unable to frame a second equation . One way would be to calculate the angle between pair of straight lines and use it to find a relation between $r$ and $h$.
However I was looking for a better solution or suggestion ?