### Video Transcript

Find the length of ππ.

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 Iβve chosen to label as the point πΆ. Weβve been asked to find the length of the line segment ππ, 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 ππ, we can find the length of ππΆ and the length of ππΆ and sum them together. Letβs think about the smaller circle first of all. The line segment ππΆ 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 weβve also been given another radius of the circle β the line ππ΄. As all of the radii of the circle are the same length, we can conclude that ππΆ is equal to ππ΄, which is seven centimetres. Now, letβs think about the larger circle. The line segment ππΆ is a radius of this circle as its endpoints are the center of the circle and a point on the circle itself.

Again, weβve been given another radius of the circle β the line segment ππ΅. As all of the radii of this circle are the same length, we can conclude that ππΆ is equal to ππ΅, which is 10 centimetres. Therefore, we have the length of ππ is ππΆ plus ππΆ, which is seven plus 10. The length of ππ is 17 centimetres.