 Hello and welcome to the session. In this session, we discuss the following question that says, given two concentric circles of radii a and b, where a is greater than b, find the length of a chord of the larger circle, which touches the other circle. Before we go on to the solution, let's discuss some results to be used in this question. First, we have a straight line drawn from the center of a circle perpendicular to a chord by such the chord, where the other result is circle, turnally, then the product of segments is the key idea that we use for this question. We proceed with the solution now. So, here we have two concentric circles and we have given that the radii are a and b, where a is greater than b. This means a is the radius of the bigger circle, that is, you can say that oa is equal to a. This is the radius of the smaller circle, that means oc is equal to b. This ab helps the larger circle, which touches the smaller circle, let this pq be the diameter of the larger circle, thus we can say pq of the larger circle. So, this is the point of intersection of the two chords pq and ab. Here we have that if two chords of the circle intersect internally or externally, then the product of the lengths of their segments are equal. Therefore, you can say that the product of the lengths of the segments of the chords ab and pq would be equal. That means the product of the lengths of the segments of the chord ab, which is ac into cb, is equal to the product of the lengths of the segments of the chord pq, which would be pc into cq. Now the pq passes through the center circle. Therefore, who is the perpendicular bisector of the chord? This means that oc would be perpendicular to ab. And we know that a straight line drawn from the center of a circle perpendicular to the chord bisects the chord. So, therefore, you can say that oc, the chord ab, this means that ac is equal to bc. So, ac into cb is equal to ac into cq can be written as ac into ac. Once ac is equal to bc, so in place of bc, or you can say cb, we write ac is equal to bc, which is op plus oc from the figure. So, op plus oc, this whole into cq, which is oq minus oc. This gives us ac square is equal to op plus oc. Op is the radius of the larger circle, which is a. So, it would be a plus oc. And this oc is the radius of the smaller circle, which is b. So, a plus b whole into oq, which is the radius of this larger circle, that is a minus oc, that is the radius of the smaller circle, which is b. So, we have ac square is equal to a square minus b square. Now, let's look at the question again. In this, we were supposed to find the length of a cord of the larger circle, which touches the other circle. That is, we are supposed to find the length of this ab. Now, further we can write, ac is equal to square root of a square minus b square. Now, since ac is equal to bc, so this means that 2 times ac would be equal to ab. So, to get the length of ab, we multiply both sides by 2. So, here we have 2 times ac is equal to 2 times of square root of a square minus b square. Now, 2 times ac means ab. So, ab is equal to 2 into square root of a square minus b square. As you can see, that the length of the cord ab is the larger circle, which touches the other circle is given by 2 into square root of a square minus b square. So, this is our final answer. This completes the session, and we have understood the solution of this question.