Video: Identifying all the Radii in a Given Circle

Identify all the radii in the following circle.

01:40

Video Transcript

Identify all the radii in the following circle.

The word radii is just a plural of the word radius. So we’re being asked to find all of the lines in the diagram, which are a radius of the given circle. Recall that the radius of a circle is any line which joins the center of the circle to a point on the circumference. The center of the circle we’ve been given is the point 𝑁. So any line which connects 𝑁 to the circumference will be a radius of this circle.

First, we note that the line segment 𝑁𝐵 is a radius of the circle as 𝑁 is the center and 𝐵 is a point on the circumference. The line segment 𝑁𝐶 is also a radius of the circle, as is the line segment 𝑁𝐸. Finally, we note that the line segment 𝑁𝐹 is also a radius of this circle. So we’ve identified four line segments which are radii of this circle, 𝑁𝐵, 𝑁𝐶, 𝑁𝐸, and 𝑁𝐹.

Let’s just have a brief look at what some of the other line segments in this circle are called. The line segments 𝐵𝐸 and 𝐹𝐶 are diameters of the circle because they each join two points on the circumference of the circle and pass through the circle’s center. The line segment 𝐹𝐷 is a chord of the circle because it joins two points on the circumference but doesn’t pass through the center of the circle.

We need to be aware of the different types of lines that exist within circles. These lines are radii, diameters, and chords, all of which we’ve seen examples of in this question.

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