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Hey, guys, we're here toe practice using our segment rules for circles. Um, so remember, there were three of them. There was an external internal, and then the tangent version of the segment rules. And so if you look a question one, here's an example of that tangent situation. Recall that if you have a basically attention seeking, like so that the segment squared equals nine times the entire length of that. Seek it. So in this case, it's gonna be 15 squared equals nine times quantity, nine plus ax. Well, that's gonna get us 15 squared, which is 2 25. Okay, equals 81 plus nine x subtracting 81. You're gonna get us 1. 44 equals nine X and then divided by nine. We're gonna get 16. Awesome. Again. I could go further and I could have asked you for like, let's say, let's say this was labeled a B. I could say Now what's the length of a B? And you could tell me 25 because 16 plus nights 25. Awesome. Okay, this problem is one of those external we have to sequence. The angle formed is outside the circle. Okay, Now we're not finding an angle, but it is an external seeking to question. And so in order for us to find X, remember that the rule is three the external part of the Secret Times. The entire seek it equals, for the external part times the entire thing. So that would be three times eight because the entire length equals four times four plus X because that's the entire lake. Alright, 24 equals 16 plus four x 24 minus 16 8 and equals four x under the words two equals x possible. And then let's look for an internal one. Okay, particularly this one. Recall that if you have two intersecting chords that this piece times this piece equals this piece times this piece. So let's do some algebra. Four x plus two times eight equals for X times. Nine. Let's do some simple fight that's 32 X Plus 16 equals 36 X That's 16 equals four X or, in other words, for equals X. Again, I could ask you for let's say, the length of each segment or part of the segments or so forth. Um, and you just plug in X for what it's worth. And of course, we could throw some or elder burn here if you wanted Thio. Let's take a look at Let's say, Let's do this question again. We have the external situation so we would say All right, four times six because it's four times the whole equals three times, the whole of the whole is gonna be what's gonna be two X plus eight because we're gonna have to add the three in the five. So we're gonna get to X plus eight. That's gonna get us six plus 24 6 packs, Apartment plus 24. All right, so that's gonna be 24 on the left hand side. Who? That's interesting. We're gonna get zero equals six X or in other words, zero equals X. That's no big deal, because what you get is just a length of five for this part of the segment, which is completely fine groups. Sorry about that. All right, let's look at this question here. Here's what we have that changing situation and recall that it's the tangent. Part squared equals the outer part times the whole. So this is gonna be interesting because it's gonna be X plus three quantity squared equals X minus three times X plus 13 Where am I getting this? X Plus 13 is because the sum of X minus three and 16 is X plus 13. So when we expand this, we get X squared plus six X plus nine equals X squared right today, X squared plus 10 X minus 39. Well, the very nice thing is, man the X where they're gonna go away. So we're left with six X plus nine equals 10 x minus 39. Okay, so if I combined, something's nine and 39 48 equals four X. So, in other words, 12 equals X. That's very nice that the exc words cancer that, if not you have a quadratic and have to solve the quadratic which could happen. That would give you their situation of 01 or two cases because of the quadratic possible solution set. All right, One more example. So recall its peace Times piece equals peace times piece. So in our case here, this would be 12 times four x plus one has to equal 14 times three plus three x, so that would be 48 x plus 12 equals what's that going to be 30? It's me. 42 plus 42 X. All right, so I'm gonna subtract. We're gonna get six X over here. We're going to get a 30 over here. X equals five. And again if we ask for, like, something like, let's find CIA. Okay. Well, I would just plug in five into here. That's gonna give me 18, and then CIA is gonna basically be 18 plus 14, which is gonna get you 32 so you could go. You know, use your theory, find your x value, and then do what it requires. That might mean plugging in doing some additional work. But this is an example of how you would use your secret and, you know, court rules. Essentially, your segment rules, um, and circles combined.

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