 Ready to start doing some geometrical problem solving? In the next three videos, we are going to discover nine different circle theorems. I'm a really big fan of them, they're just like solving little logic puzzles. Before we get started, you need to know what these words all mean. If you aren't sure, then watch this video first. In this video, we're going to look at the first four circle theorems that are all inside the circle. And then in part two and part three, there will be lots of tendons and cords involved. So let's get going. Here's the first one. What's the connection between the two angles? Hopefully, you can see that the angle at the centre is double the angle at the circumference. That's the first theorem. Sometimes this theorem can be a little disguised. See what happens when I move point B around. So if you see this sort of setup, remember that the angle at the centre is double the angle at the circumference, even if it doesn't have the normal arrowhead shape. So here's theorem two. We have a semicircle. What do you notice about the angle? The angle in a semicircle is always 90 degrees. And that's theorem two. Just make sure, though, that it really is a diameter, so it needs to cross through the centre. By the way, the number doesn't actually matter. Theorem two isn't necessarily the semicircle theorem. It's just the order that we're discovering them in this video. So here's the next one. What do you notice about the angles? Describe this one as angles in the same segment are equal. So these angles are in the major segment. But we can also describe this theorem as angles subtended by the same arc are equal. You may like to remember it as a bow tie shape, but you do need to use the key words segment or subtended by the same arc. You choose which one you think is easier to remember. So with three theorems down, here's the last one for part one. What type of shape is it and what do you notice about the angles? Four sides. So it must be a quadrilateral. But because it's inside a circle and all four corners or vertices are touching the circumference, we call it a cyclic quadrilateral. I'm sure you all spotted that the opposite angles add up to 180 degrees. So that's our fourth theorem. And the important part to remember is that all four sides must be touching the circumference for it to be a cyclic quadrilateral. So now here's the test. Can you remember all four theorems? Pause the video, jot them down and click play when you're ready to check. Make sure you use the correct terminology. Did you get them all? Check you use the correct terminology. So here are three questions for you to do using your new circle theorem knowledge. Pause the video, find the angles and click play when you're ready to check your answers. How did you get on? So there we have the first four circle theorems. Watch part two and part three to discover five more, which involve tangents and cords and take us outside of the circle.