To understand the concept that the two given circles are touches externally with each other, take an example and to show that two circles touches externally,

Consider the given circles

and

Let

and

be the centre and radius of the circle (i) respectively, now to find centre and radius compare the equation of circle with general equation of circle

to get center and radius, we have

Centre

and

Radius

Let

and

be the centre and radius of the circle (ii) respectively, now to find centre and radius compare the equation of circle with general equation of circle

to get center and radius, we have

Center

and

Radius

First we find the distance between the centers of the given circles by using the distance formula from the analytic geometry, we have

Now adding the radius of both the given circles, we have

This shows that the distance between the centres of given circles is equal to the sum of their radii. This is only possible if the circle touches each other externally as shown in the figure.

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