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The locus of the centre of a circle touc...

The locus of the centre of a circle touching the circle `x^2 + y^2 - 4y -2x = 2sqrt3 - 1` internally and tangents on which from (1,2) is making a `60^@` angle with each other is a circle. then integral part of its radius is

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`x^2+y^2-4y-2x=2sqrt3-1`
`(x-1)^2+(y-2)^2=1+4+2sqrt3-1`
`(x-1)^2+(y-2)^2=(sqrt3+1)^2`
`C_1C_2=r_1+r_2`
`(h-1)^2+(k-2)^2=(sqrt3+1+r)^2`
`sin30^0=r/(sqrt3+1+r)`
`sqrt3+1+r=2r`
`r=sqrt3+1=2.732`
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