A Nice geometry math question | solve for the radius

Hi, wonderful friends! Today we are asked to find the value of the radius of this circle. Now this circle has this triangle inscribed in it; we have five, five, six, meaning that this is an We have solved this problem before using a different method. Now we want to solve it using two different methods again, all right? So first of all I want us to recall that if you have a circle and a chord, okay, if this is the center of a circle If you draw a straight line from the center of the circle to the chord, a 90-degree angle is formed. and this point will be equal to this point, okay? All right, so if we should apply that theorem here If we apply it here now, let us drop a straight line from here to the chord. Now let's extrapolate. This is to give us this straight line, okay? Remember that the center of the circle is around here. Alright, now this is supposed to divide this place into two equal parts, which means this is three and this is three as well, okay, so this is three and this will give us three since the six six divided by two gives us three, and three, okay? Now, if we draw a line from the center of the circle to this point, we have the radius of the circle, so let's call the center of the circle, okay, all right, so we have the radius of the circle here and from here to here is another radius of the circle, but before that, let us try to find the length from a to p. Let's Call it a P to get a PIN to get a P, you know that this is a B C, okay? Now, if we draw this If we draw this, this is point P, this is point B. Now, BP is three, and AB is five. Now this. is a right angle according to our theorem, so this is a right angle. Now we are going to make use of the Pythagorean theorem now, according to Pythagoras, Pythagoras says that In a right-angled triangle with sides a and b, this side is the hypotenuse, and this side facing the right angle, and Pythagoras states that h squared is equal to a squared plus b squared All right, so that means that if we apply this theorem here, we are going to have, we are going to have the hypotenuse is five, so we are going to have five squared is equal to we have bp That's three squared plus a p squared, a p squared. All right, so five squared is 25. is equal to three squared, which is nine, plus a p squared. All right, now let's subtract nine. from both sides of this equation 25 minus nine is equal to nine plus a p squared minus Nine, okay, all right, give us a thumbs up if you're actually enjoying this video. then click the subscription button and turn on your notification bell if this is the first time you are coming across this lovely channel, all right, thank you very much, and if you're returning Viewing while returning subscriber, I appreciate all, so nine minus nine is zero, and we have that. a p is equal to 25 minus nine, which is 16. a p squared, sorry, so we take the square root of both sides. Okay, take the square root of both sides, and we have p equals the square root of 16, which is plus or minus 4. four, but we are going to take plus four because our length cannot be negative, right? So AP is four. Alright, so from here to here is four. Now this is zero. Let me write this zero somewhere here. Now from here to here is four, okay? If from here to here is four, remember that a o a o is also. The radius of the circle, OA is the radius, and OB is also the radius of the circle. All right. now if we draw out this particular right angle, let me draw it out because that is where what we are going to use to get our readings