 Hello and welcome to the session. In this session we discuss the following question that says in the given figure, that is this figure, angle A of triangle ABC is the right angle, the circle on AC as diameter cuts BC at B, if BD is equal to 3 and DC is equal to 9, calculate the length of AB. Before we move on to the solution, let's discuss some results to be used in this question. First we have the tangent at any point of a circle and the radius through this point are perpendicular to each other. Next we have a tangent externally then the product of the length of the segments of the chord is equal to the square to the point of intersection. The key idea that we use for this question. Let's proceed with the solution now. This is the figure given to us in which we have that this angle, that is angle BAC is equal to 90 degrees and the circle on AC as diameter cuts BC at D and we have BD is equal to 3 and BC is equal to 9 and we are supposed to find the length of AB. Now since we have the square A is the radius and the angle BAC is equal to 90 degrees and we know that the tangent at any point of a circle and the radius through this point are perpendicular to each other. So from this theorem we can say that AB is the tangent to the circle. So thus we have that AB is the tangent, AB is the chord of the circle and this AB and CD intersect each other externally B and from the second result stated in the key idea we have that if a chord and a tangent intersect externally then the product of the length of the segments of the chord is equal to the square of the length of the tangent from the point of contact to the point of intersection. So therefore we can say that the product of the segments of the chord CD which would be BD into BC is equal to the square of the length of the tangent which is AB square. That is we can say that AB square is equal to BD into BC. We have given that BD is equal to 3 and BC is equal to 9 and from this figure we have BC is equal to BD plus BC. BD is 3 and BC is 9. So BC is 12 and this means that AB square is equal to BD which is 3 into BC that is 12. So we have AB square is equal to 36 which means that AB is equal to 6. So this is our answer that is finally we have AB equal to a final answer. This concludes the session. Hope you understood the solution of this question.