how to apply CIRCLE THEOREM

Welcome to my channel. Okay, this is Circle Theorem. I'm going to give you detailed tutorial, okay, on how this is being solved. Now let's get to it. In this We are asked to find angle BAO. BAO. This center is O. That means we are Looking for this what? Angle. Now I want to name the angle A degrees. Okay, A degrees. easier representation. Now let's see it. First of all, look at this drawing you You might notice something that there is what? Mark here and mark here. What does that mean? It means that this triangle here, this particular triangle, is what? An isosceles. triangle. That is this place and this line, this line, and this line that they are what? Equal. And when two sides of a triangle are equal, it means that the A triangle is what? An isosceles triangle. Now there is this theorem about isosceles triangles. triangle, the base angles of an isosceles triangle are equal. Now this means that if I Is this the base angle correct? Are these two places okay? That means If I were to call this place B, it would mean that B is also equal to 35 degrees. Why? Base angles of what? Isosceles triangles have equal base angles, right? Base angles of what? Isosceles what? Triangle. That is the first thing. So we have gotten this B here. We can easily get this one here. Let's call it small d. This small d can be obtained because we've got this B and this is a triangle, and the sum of the angles in a a triangle gives us 180 degrees. What does that mean? It means that this B, which is 35 degrees to the right? This 35 degrees plus this particular C here, which is another 35 plus the d we are looking for is supposed to give us 180 degrees in this triangle. Okay? So 35 plus 35 equals 70, plus d equals 180. So What is our d? If I want this d to remain by itself, it means that this 70 will cross from here to meet 180, and if this is plus 70, if it crosses this The equation becomes minus minus 70. Okay? So it now means that this d is equal to 180 minus what? 70. So it implies that our d is equal to what? 180 minus 70 will give us 110. We are going to have 110 degrees. Okay, now we have this d to be 110 degrees. Let me write it. So but I need this angle. Remember we are looking for this A. So I I need to know this angle. I need to know this angle so I can get my A. This particular angle here, if I should call it C. Okay? For easier identification. This C and this 110 are on the same line. See what I mean? You have Something like this. This is the 110 we just found. Okay? And this is T. They are on a straight line, and there is this rule that the sum of angles on a straight line is 180 degrees. A straight line is 180. What does that mean? It implies that this C plus 110. Supposed to give us 180 degrees. So that means our C is what? 180 minus what? 110. So our C is what? 180 minus 110 will give us what? 70 degrees. If you have have followed me this far means that you truly appreciate what I'm doing. And for you to See more of this—this means you need to subscribe. Okay? Subscribe to the channel. then click on the notification bell so that you will be notified anytime I do What I uploaded is a new mathematics solution. Okay, we've determined our C to be what? 70. So this place is now 70 degrees. Don't worry, we are always almost at the solution. There is this law. Okay? A theorem that states that what? The angle on a a semicircle is 90 degrees. Remember that this is the center of the circle. So this What particular angle? It is on the semicircle. That means this angle is on The semicircle is 90 degrees. So notice that we are almost at the end of this. mathematics. This is the angle we have. Let me draw it out. This is the angle we have. have. Remember I said that here is 90 degrees? Why? Angle in a semicircle. And we have Gotten here to be 70 degrees. And we are looking for this A. Remember that angle. In a triangle, the sum of the angles is 180 degrees. So it means that A plus 90 plus 70 is supposed to give us what? 180 degrees. So A plus 90 plus 70 What is it? 160. Plus 160 is 180. So that means our A is equal to what? 180. This plus 160, we move this term to the other side of the equation to become minus 160. So it means that our A is Equal to what? 20 degrees. So have a lovely day and bye.