Question

If the two circles touches externally, then the distance between their centres is equal to
a) Difference of their radii
b) Sum of their radii
c) Product of their radii
d) None

Answer 1

Hint: Here, first we have to draw the figure of two circles having centres with A and B that touch externally at a point P. Now, join AB, which is the distance between the centres. Since P is a point on the line AB, we can write AB as:

AB = AP + PB

Complete step-by-step answer:

Here, we are given that two circles touch externally.

Now, we have to find the distance between their centres.

For that first we have to draw the figure with the given data and join AB.

In the figure we have two circles, one circle with centre A and the other circle with centre B. This two circles touch externally at a point P.
Now, we have to find the distance between their centres.
From the figure, we can say that the distance between their centres is the distance between A and B. That is AB.
Here, P is a point on the line AB.
Therefore, we can write:
AB = AP + PB
Here, AP is the radius of the circle with centre A and PB is the radius of the circle with centre B.
Hence, AB is the sum of the radii AP and PB.
Therefore, we can say that if two circles touch externally, then the distance between their centres is equal to the sum of their radii.
Hence the correct answer for this question is option (b).

Note: We also have that if the sum of the radii and the distance between their centres are equal, then the circles touch externally. If the difference between the radii and the distance between the centres are equal then the circles touch internally. Here, the circles touch externally, therefore, the distance between the centres is equal to the sum of the radii.