Question Video: Finding the Perimeter of a Triangle Whose Vertices Are the Centers of Three Externally Touching Circles Mathematics

Video Transcript

If the radius of circle 𝑀 is five centimeters and the radii of circles 𝑁 and 𝐿 are three centimeters each, find the perimeter of triangle 𝐿𝑀𝑁.

Let’s start by filling in the information that we’re given, remembering that the radius of a circle is a line segment which goes from the center of the circle to its circumference. So in this diagram, we’ll see that there are two lengths of five centimeters from the center of circle 𝑀 to the outside edge. We’re also told that circles 𝑁 and 𝐿 have radii of three centimeters each. On the diagram, this means that there will be four lengths of three centimeters.

We’re now asked to calculate the perimeter of this triangle 𝐿𝑀𝑁. And the perimeter is the distance around the outside edge. And so to find the perimeter, we add the six lengths. We have five plus three plus three plus three plus three plus five, which gives us an answer of 22. And as perimeter is a length, then we’ll still use the same units of centimeters.

And so we can give the answer that the perimeter of triangle 𝐿𝑀𝑁 is 22 centimeters.