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Question Video: Finding the Distance between the Centers of Two Circles given the Radius of One of Them Mathematics • 11th Grade

The diameter of the circle with center 𝑁 is 23, and 𝐵𝑁 = 5. Find the length of line segment 𝐴𝐵.

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Video Transcript

The diameter of the circle with center 𝑁 is 23, and 𝐵𝑁 equals five. Find the length of line segment 𝐴𝐵.

The first piece of measurement information that we’re given here is that the diameter of the circle with center 𝑁 is 23. We can remember that the diameter of a circle is a line segment passing through the center, which joins two distinct points on the circumference. This line segment 𝐴𝑁 in the figure then is not a diameter; it is, in fact, a radius. The radius of a circle is half the length of the diameter. The length of the line segment 𝐴𝑁 can therefore be found by taking half of 23, which is 11.5.

The length that we need to work out is that of the line segment 𝐴𝐵. And we can use the fact that we’re told that 𝐵𝑁 is equal to five length units. And so, the length of 𝐴𝐵 must be equal to 11.5 — that’s the length of the line segment 𝐴𝑁 — subtract five, which is equal to 6.5. Therefore, the length of the line segment 𝐴𝐵 is 6.5 and the units for that would be length units.

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