Identify all the radii of circle 𝑀.
There’s a few things we should think about here. The first thing is that when we name a circle circle 𝑀, it’s indicating to us that the point 𝑀 is the center of the circle. We also need to think about what is meant by radii. Radii is the plural form of the radius of a circle, and a radius is the distance from the center to the circumference of a circle. And the circumference is the outside edge of the circle. This means we’re looking for any line that starts at the center and goes out to the outside edge of the circle.
We see that here from 𝑀 to 𝐺, which makes line segment 𝑀𝐺 a radius, we can start at the center 𝑀 and move out to the point 𝐹, which makes the line segment 𝑀𝐹 a radius. The same thing is true if we start at the center 𝑀 and move out to the point 𝐸, which makes line segment 𝑀𝐸 a radius. 𝐹𝐺 cannot be a radius of the circle as it does not start or end at the center. It’s also worth noting that the line segment 𝐹𝐸 goes through the point 𝑀 and we call that a diameter of the circle. However, the two segments that make up the diameter are both radii. For this circle 𝑀, the three radii we see are 𝑀𝐺, 𝑀𝐹, and 𝑀𝐸.