circles(gud one!)

this is easy ..

just take centre of circle (h,r) with r as its radius as it touches the x - axis

then we can write

(x-h)² + (y-r)²=r²

further as the circle also touches y=mx

let us take tanθ=m then we have r=htan(θ/2)

substituting the value of h in the equation we get a quadratic in r ..

thus two possible radii and hence two circles

as both the circles pass through 9,6 this point should satisfy the equation ..

now substitute x=9,y=6

apply product of roots =c/a you will get tan(θ/2) AND HENCE TANθθ