Question Video: Finding the Distance between the Centers of Two Circles That Touch Externally given Their Diameters Mathematics

If the diameters of circles 𝑀 and 𝑁 are 2 cm and 6 cm, respectively, determine the length of the line segment 𝑀𝑁.

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Video Transcript

If the diameters of circles 𝑀 and 𝑁 are two centimeters and six centimeters, respectively, determine the length of the line segment 𝑀𝑁.

The line segment 𝑀𝑁 is shown. It’s a single straight line. And if we look carefully, we see that each part of the straight line is made up by joining the point at the center of each circle to a point on its circumference. That means this first part of the line segment is the radius of 𝑀. The radius of a circle is the line that joins a point on the circumference to its center. Similarly, the second part of our line segment is the radius of our circle 𝑁. This means that the line segment 𝑀𝑁 is the sum of these. It’s the length of the radius of 𝑀 plus the length of the radius of 𝑁.

Now, the problem is we’re not actually given information about the radii of our circles. We are, however, told that the diameters of our circles are two centimeters and six centimeters, respectively. Now, we know that the diameter of a circle is twice or double the length of the radius. And we can equivalently say that this means that the radius must be half the length of the diameter. Of course, to find half of a number, we divide it by two. So, this means the radius of 𝑀 is two divided by two, which is equal to one centimeter.

Similarly, we halve the length of the diameter of circle 𝑁. That’s six divided by two, which is three centimeters. So, 𝑀𝑁 is the sum of these two lengths. It’s one plus three, which is equal to four or four centimeters. The length of line segment 𝑀𝑁 is four centimeters.

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