 Hi and welcome to the session. The list has the following question. The question says in figure 10.36, this is the figure 10.36, A, B and C are three points on a circle with center O such that angle B O C is equal to 30 degree and angle A O B is equal to 60 degree. If D is a point on the circle other than the arc A, B, C find angle A, D, C. Before solving this question, we should first re-reverse with theorem 10.8 given in your book. Theorem 10.8 states that the angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle. This theorem means that if we have a circle in which our A, B subtends angle A O B at the center and angle A, C, B at point C on remaining part of the circle, then angle A O B that is angle subtended by our A, B at the center is double the angle A, C, B that is angle subtended by our A, B at point C on remaining part of the circle. The knowledge of this theorem is the key idea in this question. Let's now begin with the solution. In the question we are given that angle B O C is equal to 30 degree and angle A O B is equal to 60 degree. Now, angle A O C is equal to angle A O B plus angle B O C. Now, angle A O B is equal to 60 degree and angle B O C is equal to 30 degree. So, angle A O C is equal to 90 degree. Now, since A, B, C subtends angle A O C at the center and angle A, D, C at point C on remaining part of the circle. A O C is equal to 2 times angle A, D, C by the theorem which we have learned in key idea and which states that the angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle. We know that angle A O C is equal to 90 degree. So, now we have 90 degree is equal to 2 times angle A, D, C and this implies angle A, D, C is equal to 45 degree. Hence, angle A, D, C is equal to 45 degree. This is our required answer. So, this completes the session. I, N, J, K, L.