Learn about Diameter and Central Angle of Circles In this lesson let’s learn about diameters and central angles. We have to first find the measure of the unknown angle in this diagram or in this figure which is shown by the question mark. So, here’s where we need to learn about central angles. Central angles are any angles that are formed by two radii that meet at the center. CF is a radius. FA is a radius. FD is a radius so you get the idea. So, this is a central angle. Angle C, F, A is a central angle. So is angle A, F, D. They are all central angles. Now, here’s what I’m going to do. I’m going to actually extend this line to reach a point G. So, now I can see a plus sign dividing the circle into four equal parts. Each one of this is a right angle. It forms four different segments each at a right angle. So, the sum of all these angles of the center F is 360 degrees, 90 + 90 + 90 + 90. So, if I know that the sum of all these angles is 360 degrees and I’m giving three of them, what do I know? I can say 90 degrees + 90 degrees + 45 degrees plus the missing angle equals 360 degrees. I’ll show you how. That is just to raise the stuff on the middle. What do I see? Some of this angle plus this angle plus this angle plus this angle is the entire set of central angles. All the central angles equal 360 degrees so 90 + 90 + 45 + the missing angle is 360 which means this is 225 degrees plus the missing angle equals 360 degrees or the missing angle is 135 degrees. So, I can rate that here. So, that’s one part of the problem. Second part has to do with the diameter. If BF which is this line which is one of the radius is two feet, how long is AB? So, radius goes from the center to the edge. A diameter goes from edge to another edge but passing the center. The key thing to remember, diameter is twice the length of the radius. It makes sense, right? If this is the radius and this is also the radius, the sum of both of these is the diameter. So, the diameter is always twice the length of the radius. So, if I know the radius is 2 feet, how long is AB? That’s 4 feet because it’s twice the size of the radius. Number AB is the entire diameter, BF is just the radius.