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

Video Transcript

Find the length of 𝑀𝑁.

From the diagram, we can see that we have two circles of different sizes and their centres are the points 𝑀 and 𝑁. The two circles touch at one point, which I’ve chosen to label as the point 𝐶. We’ve been asked to find the length of the line segment 𝑀𝑁, 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 𝑀𝑁, we can find the length of 𝑀𝐶 and the length of 𝑁𝐶 and sum them together. Let’s think about the smaller circle first of all. The line segment 𝑀𝐶 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 we’ve also been given another radius of the circle — the line 𝑀𝐴. As all of the radii of the circle are the same length, we can conclude that 𝑀𝐶 is equal to 𝑀𝐴, which is seven centimetres. Now, let’s think about the larger circle. The line segment 𝑁𝐶 is a radius of this circle as its endpoints are the center of the circle and a point on the circle itself.

Again, we’ve been given another radius of the circle — the line segment 𝑁𝐵. As all of the radii of this circle are the same length, we can conclude that 𝑁𝐶 is equal to 𝑁𝐵, which is 10 centimetres. Therefore, we have the length of 𝑀𝑁 is 𝑀𝐶 plus 𝑁𝐶, which is seven plus 10. The length of 𝑀𝑁 is 17 centimetres.