Find the equation of the circle whose radius is `5` and which touches the circle `x^2+y^2-2x-4y-20=0` externally at the point `(5,5)`.

Explanation

Let the coordinates of centre of the required circle are (h, k), then the centre of another circle is (1,2).

So, it is clear that P is the mid -point of `C_(1)C_(2)`.
`therefore5=(1+h)/2rArrh=9`
and `5=(2+k)/2rArrk=8` ltbr. So, the equation of and required circle is
`(x-9)^(2)-(y-8)^(2)`=25
`rArr x^(2)-18x+81+y^(2)-16y+64=25`
`rArr x^(2)+y^(2)-18x-16y+120=0`