# Video: Finding the Sum of the Radii of Two Externally Touching Circles

Find the length of ππ.

01:58

### Video Transcript

Find the length of ππ.

From the diagram, we can see that we have two circles of different sizes and their centres are the points π and π. The two circles touch at one point, which Iβve chosen to label as the point πΆ. Weβve been asked to find the length of the line segment ππ, which is the straight line connecting the centres of the two circles and passing through the point where they touch.

To find the length of ππ, we can find the length of ππΆ and the length of ππΆ and sum them together. Letβs think about the smaller circle first of all. The line segment ππΆ is the radius of the smaller circle as its endpoints are the centre of the circle and a point on the circle itself.

We can see that weβve also been given another radius of the circle β the line ππ΄. As all of the radii of the circle are the same length, we can conclude that ππΆ is equal to ππ΄, which is seven centimetres. Now, letβs think about the larger circle. The line segment ππΆ is a radius of this circle as its endpoints are the center of the circle and a point on the circle itself.

Again, weβve been given another radius of the circle β the line segment ππ΅. As all of the radii of this circle are the same length, we can conclude that ππΆ is equal to ππ΅, which is 10 centimetres. Therefore, we have the length of ππ is ππΆ plus ππΆ, which is seven plus 10. The length of ππ is 17 centimetres.