Question

Given two circles x2+y2+5√2(x+y)=0 and x2+y2+7√2(x+y)=0. Let the radius of the third circle, which is tangent to the given circles and to their common diameter be 2P−1P then value of P/2 is

Answer 1

CD = distance between centre
CD = BD - BC $=\sqrt{(r+5{)}^2-r^2}-\sqrt{(7-r{)}^2-r^2}$
$2=\sqrt{10r+25}-\sqrt{49-14r}$
$4+49-14r+2\times 2\sqrt{49-14r}=10r+25$
$\sqrt{49-14r}=6r-7$
$49-14r=36r^2+49-84r$
$3r^2=70r$
$r=\frac{35}{18}$ $P=18$