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  4. A circle of radius 2 is touching both the axes and a circle with center (6,5). The distance between their centers is

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Q. A circle of radius $2$ is touching both the axes and a circle with center $(6,5)$. The distance between their centers is

ManipalManipal 2014

Solution:

Radius of smaller circle is $r=2\, cm$.
Since, it is touching both the axes, so its center is $(2,2)$.
image
The distance between their centers
$=r+ R=\sqrt{(5-2)^{2}+(6-2)^{2}}$
$=\sqrt{3^{2}+4^{2}}=\sqrt{25}=5$ units