The minimum distance between any two points P_1 and P_2, where P_1 lies on one circle and …

Question

The minimum distance between any two points $P_1$ and $P_2$, where $P_1$ lies on one circle and $P_2$ on the other, for the circles
$$x^2+y^2-10x-10y+41=0,\qquad x^2+y^2-24x-10y+160=0$$
is .........

Answer: 1

Accepted Answer

Circle 1: centre $(5,5)$, $r_1=3$. Circle 2: centre $(12,5)$, $r_2^2=144+25-160=9\Rightarrow r_2=3$.

Distance between centres $=7$; since $r_1+r_2=6<7$ the circles are separate, so the minimum distance is
$7-3-3=1.$

Solutions · 1