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you guys here with a couple of quick examples of some additional the're ums and properties of circles and how you can apply them very common on some standardized tests. You might have a circle here. Alright, with its center, there's a cord and we know that there's a segment that's perpendicular to the court. Then this, um, radius up to here after the side. Here's what we know. We know that the entire cord is 24 and we know this little segment here is five. The question is what is department? What is the radius of the circle? So this is a very classic example of something might see under standardized test and how to use one of these themes that we've talked about Well, recall If you have a segment that goes from the center of the circle and perpendicular to the cord, it automatically bisects the chord. So I know that the sides 12 and this side is 12. But I also want you to recall that all radio of the same circle are congruent. So if I draw this in now, I have a right triangle where this is five. This is 12, and if you recall from our birthday durian videos, and if you haven't seen that, go check it out. This is automatically 13 because five squared plus 12 squared equals 13 square. You can check it out mathematically if you want to, but that would be, um, how you find that missing side Pythagorean theorem. But 5 12 13 is a We call that the urine triples. There's one example of how you might use a serum. Here's another example again, very common on the standardized test. Might have something like, Let's say something like, Yeah, you have a couple chords, um, in the circle. And let's say I know that this angle and this angle are equal and I know that this arc right here different color. This arc right here has a measure of, let's say, 40 degrees. And the question is, what's the measure of this ark? Well, if these angles are equal, then the arcs they open up to have to be equal and you go, OK, that has to be 40 degrees a swell, because if this is 40 that would make this 20 remember all inscribed angles or half assed Muchas the ark. The intercept, which would make this 20 and then reverse that. The're, um w you get 40. So there's lots of different theories you could you could use, um, regarding, uh, tangent sequence intersecting chords, central angles, inscribed angles and have other videos that show that to specific topics. But here are a couple that are super common and all those helpful talk to later.

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